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Continuous-wave
optical parametric oscillators
and
frequency conversion sources from
the ultraviolet to the mid-infrared
Kavita Devi
Universitat Politecnica de Catalunya
Barcelona, May 2013
Doctorate Program: Photonics
Duration: 2009-2013
Thesis advisor: Prof. Majid Ebrahim-Zadeh
Thesis submitted in partial fulfillment of the requirements for the
degree of Doctor of Philosophy of the Universitat Politecnica de
Catalunya
May 2013
Dedicated to my loving parents
Declaration
I hereby declare that the matter embodied and presented in the thesis entitled, “Continuous-wave optical parametric oscillators and frequency
conversion sources from the ultraviolet to the mid-infrared” is the
result of investigations carried out by me at the ICFO-Institute of Photonic
Sciences, Castelldefels, Barcelona, Spain under the supervision of Prof. Majid
Ebrahim-Zadeh, and that it has not been submitted elsewhere for the award
of any degree or diploma. In keeping with the general practice in reporting
scientific observations, due acknowledgment has been made whenever the work
described is based on the findings of other investigators.
———————————
Kavita Devi
Certificate
I hereby certify that the matter embodied and presented in this thesis entitled, “Continuous-wave optical parametric oscillators and frequency
conversion sources from the ultraviolet to the mid-infrared” has been
carried out by Miss Kavita Devi at the ICFO-Institute of Photonic Sciences,
Castelldefels, Barcelona, Spain, under my supervision, and that it has not been
submitted elsewhere for the award of any degree or diploma.
——————————————
Prof. Majid Ebrahim-Zadeh
(ICFO, Research Supervisor)
Acknowledgements
I am pleased to acknowledge the many individuals, for their support and assistance in different aspects, during the course of this doctoral studies.
First of all, I would like to express my sincere gratitude to Prof. Majid
Ebrahim-Zadeh for his guidance, advice, and invaluable ideas, without which
this thesis would not have been possible. He has not only supervised me, but
has also provided me the enourmous encouragement and support, that gave
me enthusiasm and confidence to face a new challenge at any time. His vast
knowledge in broader field of science and technology together with industrial
experience enriched my growth as a researcher. His ever friendly attitude gave
me the freedom to express, explore and implement new ideas. I am indebted
to him more than he knows.
I am very grateful to have a wonderful group of labmates. My special thanks
goes to Goutam, Adolfo, Chaitanya, Ramaiah, Ossi, Enrique and Stefano, for
creating such a great environment in the lab, sharing instruments, thoughts
and expertise. The discussions and collaborations with Goutam and Chaitanya
have been fruitful during the last years. I would like to extend my special
thanks to Chaitanya for always providing me a helping hand, and to Adolfo
for helping me translate the abstract of this thesis into Spanish.
I want to express my gratitude to Prof. Luis Torner, Director of the ICFOInstitute of Photonic Sciences, and his management team for making ICFO
such a wonderful place for research. The efficiency of the human resource
team, purchasing unit, mechanical and electronic workshop, and knowledge
and technology transfer unit helped me to concentrate fully on my research.
I am grateful to all my teachers and professors in the school, college and
IIT Guwahati for sharing their immense knowledge in wide range of fields
and preparing me for the advanced studies. I express my thanks to Prof. A.
Khare, Dr. S. Khijwania and Dr. P. Poulose for their belief in me. I would
also like to thank my friends, Rajan(bhaiya), Ritwick(bhaiya), Joyee(didi),
Arpita, Saurabh, Arup, Anshuman, and including my MSc and BSc friends
for sharing their scientific as well as non-scientific views. I can not put my
thoughts and feelings into words, when it comes to thank Dhriti. Despite his
own busy research schedule, he has always been supportive in every aspects.
My heartiest thanks goes to him, for his patience, time, affection and support.
My everlasting gratitude goes to my mother, Rumi Devi and father, Rajendra Nath Sharma for their unconditional and continuous love and support.
They are the ones who initiated the intellectual development in me. They have
always been my inspiration and a guiding light. Special thanks to my sisters
Gitali and Mitu, for being supportive and caring.
Abstract
High-power, continuous-wave (cw) optical parametric oscillators (OPOs), from
the ultraviolet (UV) and visible to the near- and mid-infrared (IR) wavelength
range, are of interest for a variety of applications such as spectroscopy, tracegas detection and remote sensing. As such, it is desired to investigate OPOs
and different frequency conversion techniques, to cover the spectral regions
that are inaccessible to lasers, and that too in a compact and low-cost design.
This thesis presents the development of high-power cw OPOs, and frequency conversion sources, spanning the UV to mid-IR spectral range, employing different designs, experimental configurations and nonlinear crystals,
making them compact and cost-effective. Commercial high-power cw lasers at
1940 nm, 1064 nm and 532 nm have been exploited as the pump sources, in
the work presented in this thesis.
We have demonstrated a fiber-based cw source at 970 nm, in a simple and
practical design. Using direct single-pass second-harmonic-generation (SHG),
13.1 W of output power at 970 nm has been generated in a high-beam-quality,
narrow-linewidth, linearly-polarized beam. Further, a technique based on the
use of an antiresonant ring (ARR) interferometer for the attainment of optimum output coupling in a cw singly-resonant OPO has been investigated.
The technique was deployed in a Yb-fiber-laser-pumped cw OPO based on
MgO:PPLN. To extend the tunability of the 1-µm-pumped OPO from the midIR to near-IR, SHG of the intracavity signal has been performed in fanoutgrating MgO:sPPLT. This compact cw source, tunable across 775–807 nm,
provides >3 W of near-infrared power across 56% of SHG tuning range, in
high spatial beam quality. We have also generated output in the UV, down
to 355 nm, using single-pass configuration based on sum-frequency-generation
of fundamental at 1064 nm and the generated SHG at 532 nm, in BiB3 O6 .
Further, we demonstrated an architecture comprising two cw OPOs coupled
together with an ARR interferometer, generating two pairs of signal and idler
wavelengths, that can be independently and arbitrarily tuned to indefinitely
close spacing, through degeneracy, and beyond, across the wavelength range
of 870-1370 nm. The OPOs, based on identical MgO:sPPLT crystals, were
pumped by a single cw laser at 532 nm. On the other hand, we also demonstrated active mode-locking of cw OPOs using direct low-frequency electrooptic phase-modulation (EOM), opening up the possibility of avoiding the
need for ultrafast laser sources and synchronous pumping. We have generated picosecond pulses in doubly- and singly-resonant configuration. Also, a
technique based on the deployment of the EOM in combination with an ARR
interferometer internal to the cw OPO has been investigated for active modelocking.
Resumen
Los osciladores ópticos paramétricos (OPOs) de onda continua (cw) y alta
potencia en el rango espectral ultravioleta (UV), visible e infrarrojo cercano y
medio (IR), son de gran interés para una gran variedad de aplicaciones como:
espectroscopia, detección de gases y sensores remotos. Por lo tanto, es vital la
investigación en OPOs y diferentes técnicas de conversión de frecuencias con
el objetivo de cubrir las regiones espectrales inaccesibles a los láseres, así como
lograr diseños compactos y de bajo coste.
Esta tesis presenta el desarrollo de cw OPOs de alta potencia y fuentes de
conversión de frecuencias, expandiendo el rango espectral desde el UV hasta
el IR medio, empleando diferentes diseños, configuraciones experimentales y
cristales no lineales, resultando en diseños compactos y de bajo coste. En el
trabajo presentado en esta tesis, se han utilizado como fuentes de bombeo
láseres comerciales de alta potencia a 1940 nm, 1064 nm y 532 nm.
Hemos demostrado una fuente basada en fibra a 970 nm con un diseño
simple y práctico. Utilizando directamente generación de segundo armónico
(SHG) en un paso, se ha logrado generar 13.1 W de potencia de salida a 970
nm con un haz de alta calidad, ancho de línea estrecho y polarización lineal.
Adicionalmente, se ha investigado una técnica que emplea un interferómetro
de anillo antiresonante (ARR) para conseguir acoplamiento de salida óptimo
en un cw OPO simplemente resonante. Esta técnica fue implementada en un
cw OPO basado en MgO:PPLN y bombeado por un láser de fibra Yb. Con
el objetivo de expandir la sintonización del OPO bombeado a 1 µm desde el
IR medio al IR cercano, se ha implementado SHG de la señal intracavidad
utilizando MgO:sPPLT con una red fanout. El resultado es una fuente cw
compacta, sintonizable en el rango 775–807 nm, con potencias del infrarrojo
cercano >3 W a lo largo del 56% del rango de sintonización de SHG y con
alta calidad espacial del haz. También hemos generado salida en el UV hasta
los 355 nm, utilizando una configuración de paso único en BiB3 O6 para generación de suma de frecuencias entre la fundamental a 1064 nm y la de SHG
generada a 532 nm. Además, demostramos una arquitectura incluyendo dos
cw OPOs acoplados con un interferómetro ARR, generando dos pares de longitudes de onda señal y idler que pueden ser independiente y arbitrariamente
sintonizadas, incluso hasta la degeneración y más allá, a lo largo del rango de
longitudes de onda 870-1370 nm. Los OPOs utilizan dos cristales idénticos de
MgO:sPPLT y fueron bombeados por un cw laser a 532 nm. Por otra parte,
también demostramos mode-locking activo de un cw OPO utilizando directamente modulación de fase electroóptica (EOM) de baja frecuencia, abriendo
la posibilidad de evitar la necesidad de uso de fuentes láser ultrarrápidas y
bombeos sincronizados. Mediante esta técnica, hemos generado pulsos de picosegundos tanto en configuraciones doble y simplemente resonantes. Adicionalmente, se ha investigado ora técnica que integra un EOM combinado
con un interferómetro ARR dentro de la cavidad del cw OPO con el objetivo
de conseguir mode-locking activo.
Publications
Journal publications
1. K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh, “Mode-locked
continuous-wave mid-infrared optical parametric oscillator: pulse formation and spectral characterization,” To be submitted (2013).
2. K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh, “Tunable continuous-
wave, ultraviolet source based on intracavity sum-frequency-generation in
an optical parametric oscillator,” Opt. Express, submitted (2013).
3. K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh, “Directly phase-
modulation-mode-locked doubly-resonant optical parametric oscillator,”
Opt. Express, submitted (2013).
4. S. Chaitanya Kumar, K. Devi, and M. Ebrahim-Zadeh, “Stable, continuous-
wave, Yb-fiber-based single-pass ultraviolet source,” Opt. Letters, submitted (2013).
5. K. Devi, S. Chaitanya Kumar, A. Esteban-Martin, and M. Ebrahim-
Zadeh, “Dual-wavelength interferometrically-coupled continuous-wave optical parametric oscillator,” Laser and Photonics Reviews, submitted (2013).
6. K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh, “High-power,
continuous-wave, single-frequency, all-periodically-poled, near-infrared source,”
Opt. Letters 37, 5049-5051 (2012).
7. K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh, “Mode-locked,
continuous-wave, singly resonant optical parametric oscillator,” Opt. Letters 37, 3909-3911 (2012).
8. K. Devi, S. Chaitanya Kumar, A. Esteban-Martin, and M. Ebrahim-
Zadeh, “Antiresonant ring output-coupled continuous-wave optical parametric oscillator,” Opt. Express 20, 19313-19321 (2012).
9. A. Esteban-Martin, G. K. Samanta, K. Devi, S. Chaitanya Kumar, and
M. Ebrahim-Zadeh, “Frequency-modulation-mode-locked optical parametric oscillator,” Opt. Letters 37, 115-117 (2012).
(Among Top-10 downloaded articles (OSA) in Jan, 2012.)
10. S. Chaitanya Kumar, G. K. Samanta, K. Devi, S. Sanguinetti, and
M. Ebrahim-Zadeh, “Single-frequency, high-power, continuous-wave fiberlaser-pumped Ti:sapphire laser,” Appl. Optics 51, 15-20 (2012).
(Selected for the cover page of the 50th Anniversary issue; Among Top-10
downloaded articles (OSA) in the year 2012.)
11. G. K. Samanta, S. Chaitanya Kumar, K. Devi, and M. Ebrahim-Zadeh,
“High-power, continuous-wave Ti:sapphire laser pumped by fiber-laser
green source at 532 nm,” Optics and Lasers in Engineering 50, 215-219
(2012).
12. K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh, “13.1 W, high-
beam-quality, narrow-linewidth continuous-wave fiber-based source at 970
nm,” Opt. Express 19, 11631-11637 (2011).
(Selected for July issue of Virtual Journal of Biomedical Optics, 6(7),
2011.)
13. S. Chaitanya Kumar, G. K. Samanta, K. Devi, and M. Ebrahim-Zadeh,
“High-efficiency, multicrystal, single-pass, continuous-wave second harmonic generation,” Opt. Express 19, 11152-11169 (2011).
14. S. Chaitanya Kumar, K. Devi, G. K. Samanta, and M. Ebrahim-Zadeh,
“Fiber-laser-based green-pumped continuous-wave singly-resonant optical
parametric oscillator,” Journal of Laser Physics 21, 782-789 (2011).
15. G. K. Samanta, S. Chaitanya Kumar, K. Devi, and M. Ebrahim-Zadeh,
“Multi-crystal, continuous-wave, single-pass second-harmonic-generation
with 56% efficiency,” Opt. Letters 35, 3513-3515 (2010).
(Highlighted in Laser Focus World, Jan 2011; Among Top-10 downloaded
articles over two years, 2011-2012.)
Proceeding publications
1. K. Devi, S. Chaitanya Kumar, G. K. Samanta, A. Esteban-Martin, and
M. Ebrahim-Zadeh, “Continuous-wave mode-locked optical parametric
oscillator,” Proc. SPIE 8434, 84340D (2012).
2. K. Devi, S. Chaitanya Kumar, A. Esteban-Martin, and M. Ebrahim-
Zadeh, “Interferometeric output coupling of a continuous-wave optical
parametric oscillator,” Proc. SPIE 8434, 84340E (2012).
3. K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh, “High-beam-
quality, narrow-linewidth, 13 W continuous-wave fiber-based source at
970 nm,” Proc. SPIE 8434, 843405 (2012).
4. K. Devi, S. Chaitanya Kumar, G. K. Samanta, and M. Ebrahim-Zadeh,
“Highly efficient continuous-wave single-pass second-harmonic generation
using multicrystal scheme,” Proc. SPIE 8173, 81730K (2010).
5. K. Devi, S. Chaitanya Kumar, G. K. Samanta, and M. Ebrahim-Zadeh,
“Continuous-wave-fiber-laser-pumped Ti:sapphire laser,” Proc. SPIE 8173,
81730J (2010).
Conference publications
1. K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh, “Actively mode-
locked continuous-wave singly-resonant mid-infrared optical parametric
oscillator,” MICS, Paris, France, October 2013.
2. K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh, “Stable, continuous-
wave, fiber-laser-based, ultraviolet generation in BiB3 O6 ,” CLEO/EuropeEQEC, Munich, Germany, May 2013.
3. V. Ramaiah Badarla, K. Devi, S. Chaitanya Kumar, A. Esteban-Martin,
and M. Ebrahim-Zadeh, “Interferometrically coupled two-color femtosecond optical parametric oscillator,” International Conference on Fiber Optics and Photonics, Chennai, India, December 2012.
4. K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh, “Frequency-
modulation-mode-locked singly-resonant optical parametric oscillator,”
NLO 50 International Symposium, Barcelona, Spain, October 2012.
5. K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh, “Tunable, high-
power, all-periodically-poled, continuous-wave, intracavity-frequency-doubled
optical parametric oscillator,” 5th EPS-QEOD Europhoton Conference,
Stockholm, Sweden, August 2012.
6. K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh, “Actively mode-
locked optical parametric oscillator using low-frequency phase-modulation,”
Conf. Lasers and Electro-Optics (CLEO), San Jose, California, USA, May
2012.
7. K. Devi, V. Ramaiah-Badarla, S. Chaitanya Kumar, A. Esteban-Martin,
and M. Ebrahim-Zadeh, “Dual-wavelength, interferometrically coupled
continuous-wave optical parametric oscillators,” Conf. Lasers and ElectroOptics (CLEO), San Jose, California, USA, May 2012.
8. K. Devi, S. Chaitanya Kumar, A. Esteban-Martin, and M. Ebrahim-
Zadeh, “Interferometrically output-coupled continuous-wave optical parametric oscillator,” Conf. Lasers and Electro-Optics (CLEO), San Jose,
California, USA, May 2012.
9. K. Devi, S.Chaitanya Kumar, G. K. Samanta, A. Esteban-Martin, and
M. Ebrahim-Zadeh, “Continuous-wave mode-locked optical parametric
oscillator,” SPIE Photonics Europe, Brussels, Belgium, April 2012.
10. K. Devi, S.Chaitanya Kumar, A. Esteban-Martin, and M. Ebrahim-
Zadeh, “Interferometeric output coupling of a continuous-wave optical
parametric oscillator,” SPIE Photonics Europe, Brussels, Belgium, April
2012.
11. K. Devi, S.Chaitanya Kumar, and M. Ebrahim-Zadeh, “High-beam-
quality, narrow-linewidth, 13 W continuous-wave fiber-based source at
970 nm,” SPIE Photonics Europe, Brussels, Belgium, April 2012.
12. S. Chaitanya Kumar, G. K. Samanta, K. Devi, S. Sanguinetti, and M.
Ebrahim-Zadeh, “High-power, single-frequency Ti:sapphire laser pumped
by a continuous-wave fiber laser green source,” CLEO/Europe-EQEC,
Munich, Germany, May 2011.
13. K. Devi, S. Chaitanya Kumar, G. K. Samanta, and M. Ebrahim-Zadeh,
“Highly efficient continuous-wave single-pass second-harmonic generation
using multicrystal scheme,” International Conference on Fiber Optics and
Photonics, Guwahati, India, December 2010.
14. K. Devi, S. Chaitanya Kumar, G. K. Samanta, and M. Ebrahim-Zadeh,
“Continuous-wave-fiber-laser-pumped Ti:sapphire laser,” International Conference on Fiber Optics and Photonics, Guwahati, India, December 2010.
15. G. K. Samanta, S. Chaitanya Kumar, K. Devi, and M. Ebrahim-Zadeh,
“55%-efficient, 13-W, single-pass SHG of a cw Yb-fiber laser in a doublecrystal scheme,” Conf. Lasers and Electro-Optics (CLEO), San Jose,
California, USA, May 2010.
16. G. K. Samanta, S. Chaitanya Kumar, K. Devi, and M. Ebrahim-Zadeh,
“Fiber-laser-pumped Ti:sapphire laser,” Conf. Lasers and Electro-Optics
(CLEO), San Jose, California, USA, May 2010.
Contents
1 Introduction
19
2 Basics of nonlinear optics
29
2.1
The origin of optical nonlinearity . . . . . . . . . . . . . . . . . 29
2.2
Second-order nonlinear susceptibility . . . . . . . . . . . . . . . 30
2.3
Second-order nonlinear optical interactions . . . . . . . . . . . . 31
2.4
Coupled-wave equations for second-order nonlinear processes . . 33
2.5
Phase-matching . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.5.1
Birefringent phase-matching . . . . . . . . . . . . . . . . 36
2.5.2
Quasi-phase-matching . . . . . . . . . . . . . . . . . . . 40
2.6
Second-harmonic and sum-frequency-generation . . . . . . . . . 41
2.7
Optical parametric oscillator . . . . . . . . . . . . . . . . . . . . 43
2.7.1
Parametric gain and amplification
. . . . . . . . . . . . 43
2.7.2
Oscillator configurations . . . . . . . . . . . . . . . . . . 45
2.7.3
Steady-state threshold in cw OPOs . . . . . . . . . . . . 45
2.7.4
Wavelength tuning . . . . . . . . . . . . . . . . . . . . . 47
2
Contents
2.8
Nonlinear materials . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.9
Cavity design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.10 Active mode-locking . . . . . . . . . . . . . . . . . . . . . . . . 53
3 High-power, cw, fiber-based source at 970 nm
57
3.1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2
Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3
Results and discussion . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.1
Optimization of the SHG operation . . . . . . . . . . . . 60
3.3.2
Variation in phase-matching temperature with beam waist 61
3.3.3
Variation in phase-matching temperature with pumping
level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.4
3.3.4
Temperature acceptance bandwidth . . . . . . . . . . . . 64
3.3.5
SHG power scaling and stability . . . . . . . . . . . . . . 66
3.3.6
SHG single-frequency operation and beam quality . . . . 68
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4 Interferometrically output-coupled cw SRO
73
4.1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2
ARR output-coupled cw SRO . . . . . . . . . . . . . . . . . . . 76
4.3
4.2.1
Experimental setup . . . . . . . . . . . . . . . . . . . . . 76
4.2.2
Design and optimization of the cavity . . . . . . . . . . . 78
Results and discussion . . . . . . . . . . . . . . . . . . . . . . . 79
Contents
4.4
3
4.3.1
Conventional 5% output-coupled SRO . . . . . . . . . . 79
4.3.2
Variable output coupling . . . . . . . . . . . . . . . . . . 79
4.3.3
Output coupling optimization at different pumping levels 81
4.3.4
Power scaling . . . . . . . . . . . . . . . . . . . . . . . . 84
4.3.5
Pump depletion, threshold pump power and beam quality 88
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5 All-periodically-poled, tunable, cw, near-infrared source
93
5.1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2
Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3
Results and discussion . . . . . . . . . . . . . . . . . . . . . . . 97
5.4
5.3.1
Power across the tuning range . . . . . . . . . . . . . . . 97
5.3.2
Power scaling . . . . . . . . . . . . . . . . . . . . . . . . 99
5.3.3
Power stability . . . . . . . . . . . . . . . . . . . . . . . 100
5.3.4
Single-frequency operation and beam quality . . . . . . . 102
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6 Continuous-wave ultraviolet source based on BiB3 O6
105
6.1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2
Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.3
Results and discussion . . . . . . . . . . . . . . . . . . . . . . . 111
6.3.1
Power scaling . . . . . . . . . . . . . . . . . . . . . . . . 111
6.3.2
Power stability and spectrum . . . . . . . . . . . . . . . 112
4
Contents
6.3.3
6.4
Frequency stability and beam quality . . . . . . . . . . . 113
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7 Dual-wavelength, ARR-coupled, cw OPO
117
7.1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2
Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.3
Results and discussion . . . . . . . . . . . . . . . . . . . . . . . 121
7.4
7.3.1
Charaterization of the ARR interferometer
. . . . . . . 121
7.3.2
Tuning capability of ARR-coupled cw OPO . . . . . . . 122
7.3.3
Single-frequency operation . . . . . . . . . . . . . . . . . 124
7.3.4
Power scaling . . . . . . . . . . . . . . . . . . . . . . . . 125
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
8 Mode-locked, cw OPOs
129
8.1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
8.2
External charaterization of the EOM . . . . . . . . . . . . . . . 132
8.3
Mode-locking of cw DRO using ARR interferometer . . . . . . . 135
8.4
8.3.1
Experimental setup . . . . . . . . . . . . . . . . . . . . . 135
8.3.2
Phase-to-amplitude modulation conversion . . . . . . . . 138
8.3.3
Mode-locked pulse generation . . . . . . . . . . . . . . . 140
8.3.4
Output spectrum . . . . . . . . . . . . . . . . . . . . . . 143
8.3.5
Confirmation of true mode-locked operation . . . . . . . 143
Phase-modulation-mode-locked cw DRO . . . . . . . . . . . . . 145
Contents
8.5
5
8.4.1
Experimental setup . . . . . . . . . . . . . . . . . . . . . 145
8.4.2
Output power and threshold . . . . . . . . . . . . . . . . 146
8.4.3
Mode-locked pulse generation . . . . . . . . . . . . . . . 147
8.4.4
Power stability . . . . . . . . . . . . . . . . . . . . . . . 150
8.4.5
Pulse width dependence on the position of EOM . . . . . 151
8.4.6
Pulse width dependence on pumping level . . . . . . . . 152
8.4.7
Output spectrum . . . . . . . . . . . . . . . . . . . . . . 152
8.4.8
Confirmation of true mode-locked operation . . . . . . . 154
Phase-modulation-mode-locked cw SRO
. . . . . . . . . . . . . 155
8.5.1
Experimental setup . . . . . . . . . . . . . . . . . . . . . 155
8.5.2
Mode-locked pulse generation . . . . . . . . . . . . . . . 156
8.5.3
Output spectrum . . . . . . . . . . . . . . . . . . . . . . 160
8.5.4
Pulse stability, and confirmation of true mode-locked
operation . . . . . . . . . . . . . . . . . . . . . . . . . . 161
8.6
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
9 Summary and outlook
165
Bibliography
169
List of Tables
2.1
Characterization of some nonlinear crystals. VTE-SLT: Vapor
transport equilibration stoichiometric LiTaO3 , SLT: Stoichiometric LiTaO3 , MCLT: MgO-doped congruent LiTaO3 , VTECLT: Vapor transport equilibration congruent LiTaO3 , SLN:
Stoichiometric LiNbO3 .
. . . . . . . . . . . . . . . . . . . . . . 50
2.2
Ray matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6.1
Phase-matching (PM) properties of some nonlinear crystals for
UV generation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
List of Figures
1.1
Spectral coverage of conventional tunable lasers. . . . . . . . . . 20
1.2
Spectral tuning available from OPOs. . . . . . . . . . . . . . . . 20
1.3
Approach of the thesis research work. . . . . . . . . . . . . . . . 24
2.1
Schematic of various second-order nonlinear processes. (a) SFG,
(b) SHG, (c) DFG, (d) OPG, and (e) OPO. . . . . . . . . . . . 32
2.2
Generated wave intensity as a function of propagation distance
in nonlinear crystal for (a) perfectly phase-matched (∆k = 0),
(b) non-phase-matched (∆k 6= 0), and (c) quasi-phase-matched
conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3
Index ellipsoids for (a) positive uniaxial crystals and (b) negative uniaxial crystals. . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4
Illustration of birefringent phase-matching for SHG in uniaxial
crystal.
2.5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Schematic of wave propagation for biaxial crystal, in the crystal
coordinate system. . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.6
(a) Periodic inversion of the sign of the nonlinear coefficient,
and (b) fanout grating structure, in a QPM nonlinear material.
41
10
List of Figures
2.7
Cavity configurations for OPOs: (a) singly-resonant (SRO),
(b) doubly-resonant (DRO), (c) triply-resonant (TRO), and (d)
pump-enhanced (PE-SRO). . . . . . . . . . . . . . . . . . . . . 46
2.8
The tuning curves for signal and idler wavelengths for a 1-µmpumped MgO:PPLN OPO. . . . . . . . . . . . . . . . . . . . . . 48
2.9
Various OPO cavity designs: (a) Linear cavity, (b) V-cavity, (c)
X-cavity, (d) Ring cavity. . . . . . . . . . . . . . . . . . . . . . . 52
2.10 Signal beam waist along the ring cavity. . . . . . . . . . . . . . 54
3.1
Schematic of the experimental setup. . . . . . . . . . . . . . . . 60
3.2
SHG efficiency at maximum fundamental power, as a function
of focusing parameter, x=l/b. . . . . . . . . . . . . . . . . . . . 61
3.3
(a) Phase-matching temperature at maximum fundamental power,
as a function of focusing parameter, x. (b) Theoretically calculated propagation length for divergent components and the corresponding change in phase-matching temperature, as a function of beam waist radius. (c) Theoretically calculated phasematching temperature, as a function of focusing parameter, x.
(d) Phase-matching temperature under different focusing conditions, at pump power of ∼1W. . . . . . . . . . . . . . . . . . . 63
3.4
(a) Phase-matching temperature versus fundamental power. (b)
Theoretically calculated change in phase-matching temperature
versus fundamental wavelength for the grating period of Λ=28.2
µm.
3.5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
(a) Temperature phase-matching curve for SHG at w o ∼45 µm,
and (b) temperature acceptance bandwidth under different focusing conditions. Pump power is ∼1 W. . . . . . . . . . . . . . 67
List of Figures
3.6
11
SHG power and the corresponding conversion efficiency as a
function of incident fundamental power at w o ∼45 µm. . . . . . . 68
3.7
Time trace at maximum power of (a) generated SHG output,
and (b) input fundamental over 1 hour. . . . . . . . . . . . . . . 69
3.8
Spectrum of SHG output at maximum power. . . . . . . . . . . 70
3.9
Far-field TEM00 energy distribution of the generated SHG beam.
The thin curves are the intensity profiles along the two orthogonal axes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.1
Antiresonant ring interferometer. . . . . . . . . . . . . . . . . . 76
4.2
Schematic of the experimental setup. FI: Faraday isolator, λ/2:
Half-wave plate, PBS: Polarizing beam-splitter, L: Lens, M1−5 :
Mirrors, M: Dichroic mirror, BS: Beam-splitter. . . . . . . . . . 77
4.3
Variation of signal and idler power along with the total power
extracted from the OPO using conventional 5% OC as a function
of input pump power. . . . . . . . . . . . . . . . . . . . . . . . . 80
4.4
Transmission from ARR interferometer as a function of BS angle, θBS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5
Optimization of signal power versus BS angle, θBS , at input
pump power of (a) 15.9 W, and (b) 23.2 W. . . . . . . . . . . . 82
4.6
Optimization of simultaneously extracted single-pass idler power
versus BS angle, θBS , at input pump power of (c) 15.9 W, and
(d) 23.2 W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.7
Theoretically calculated optimization curves for signal and idler
power as a function of output coupling at input pump power of
(a) 15.9 W, and (b) 23.2 W. . . . . . . . . . . . . . . . . . . . . 85
12
List of Figures
4.8
Theoretically calculated optimization curves for signal power as
a function of output coupling at low pump power of 5 W and
high pump power of 28.6 W. . . . . . . . . . . . . . . . . . . . . 86
4.9
Signal and corresponding idler along with total output power
scaling at BS angle, θBS =33o . . . . . . . . . . . . . . . . . . . . 87
4.10 Signal power scaling at optimum signal output coupling values.
Inset: Corresponding theoretical plot. . . . . . . . . . . . . . . . 88
4.11 Idler power scaling at minimum signal output coupling values.
Inset: Corresponding theoretical plot. . . . . . . . . . . . . . . . 89
4.12 Pump depletion as a function of BS angle, θBS , at input pump
power of 23.2 W. . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.13 The cw SRO threshold power, P th , as a function of signal output
coupling with the ARR. Inset: far-field energy distribution of
extracted signal with optimum ARR-OC value of 4.6% at 23.2
W of input pump power. . . . . . . . . . . . . . . . . . . . . . . 91
5.1
Schematic of the intracavity frequency-doubled cw OPO. FI:
Faraday isolator, λ/2: Half-wave plate, PBS: Polarizing beamsplitter, L: lens, M1−6 : Cavity mirrors, M0 and M00 : Dichroic
mirrors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2
Photograph of the all-periodically-poled, near-infrared source
operating in our laboratory. . . . . . . . . . . . . . . . . . . . . 97
5.3
Variation of SHG power as a function of SHG wavelength. . . . 98
5.4
Theoretical SHG (a) grating tuning range and (b) temperature
tuning range in present setup. . . . . . . . . . . . . . . . . . . . 99
List of Figures
5.5
13
Variation of idler power and corresponding pump depletion across
the idler tuning range. . . . . . . . . . . . . . . . . . . . . . . . 99
5.6
Variation of (a) SHG power, idler output power, pump depletion, and (b) signal power as a function of pump power. . . . . . 101
5.7
Simultaneously recorded passive power stability of (a) SHG and
(b) idler output from the SRO. . . . . . . . . . . . . . . . . . . 102
5.8
Single-frequency spectrum of generated SHG at 801 nm for
pump power of 27.4 W. . . . . . . . . . . . . . . . . . . . . . . . 103
5.9
Far-field energy distribution of generated SHG at 801 nm for
pump power of 27.4 W. . . . . . . . . . . . . . . . . . . . . . . . 103
6.1
Schematic of experimental setup for the fiber-laser-based singlepass UV source. FI: Faraday isolator, λ/2: Half-wave plate,
PBS: Polarizing beam-splitter, L: Lens, M: Mirrors, F: Filter. . . 110
6.2
Picture of the cw UV source operating in our laboratory (left)
and the generated UV beam (right).
6.3
. . . . . . . . . . . . . . . 110
Variation of the cw UV power as a function of fundamental
power at the output of the SFG stage. . . . . . . . . . . . . . . 112
6.4
Dependence of the measured cw SHG power and the corresponding conversion efficiency on the incident fundamental power at
the output of SHG stage. . . . . . . . . . . . . . . . . . . . . . . 112
6.5
UV output power stability at 50 mW over >2 hours. Inset: UV
spectrum measured at maximum output power. . . . . . . . . . 114
6.6
Long-term frequency stability of the generated UV output at
354.7945 nm, over a period of >2.5 hours. . . . . . . . . . . . . 114
14
List of Figures
6.7
Far-field energy distribution and intensity profiles of the generated UV beam at maximum output power. . . . . . . . . . . . . 115
7.1
Experimental setup of the ARR-coupled cw OPO. H1−3 : Halfwave plates, PBS: Polarizing beam-splitter, P1 , P2 : Pump beams,
L1,2 : Lens, M1−9 : Cavity mirrors, X1,2 : MgO:sPPLT crystals,
M: Dichroic mirrors, BS: Beam-splitter, λ1s , λ2s : Dual signal
wavelengths leaked through M3 , I1,2 : Idler beams. . . . . . . . . 120
7.2
Picture of the ARR-coupled cw OPO operating in our laboratory.121
7.3
Transmission of the ARR interferometer as a function of BS angle.122
7.4
Direction of the dual wavelength signal beams to and from the
OPOs, and within the ARR. . . . . . . . . . . . . . . . . . . . . 123
7.5
Signal spectra from the ARR-coupled, dual-wavelength OPO at
independently tunable crystal temperatures, T1 and T2 . . . . . . 124
7.6
Fabry-Perot transmission spectra of the dual signal wavelengths. 125
7.7
(a) Idler output power from OPO-1 and OPO-2 versus pump
power, with both OPOs in simultaneous operation. (b) Power
scaling of OPO-2 without the ARR. . . . . . . . . . . . . . . . . 126
8.1
Single-pass EOM output spectrum (a) at ν=80 MHz for different modulation depth (µ1 <µ2 <µ3 <µ4 <µ5 ) of (i) µ1 (ii) µ2 (iii)
µ3 (iv) µ4 (v) µ5 and (b) for fixed modulation depth of µ3 at
different modulation frequency (ν1 <ν2 <ν<ν3 <ν4 ) of (i) ν1 (ii)
ν2 (iii) ν (iv) ν3 (v) ν4 . . . . . . . . . . . . . . . . . . . . . . . . 134
8.2
Bessel function amplitude of order 0, 1, 2 and 3, representing
the amplitudes of carrier frequency, 1st , 2nd , and 3rd side bands,
respectively, with modulation depth as argument. . . . . . . . . 135
List of Figures
8.3
15
Schematic of the continuous-wave, mode-locked DRO. λ/2: Halfwave plate, PBS: Polarizing beam-splitter, L: Lens, M1−6 : Cavity mirrors, EOM: Electro-optic phase modulator, BS: Beamsplitter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8.4
Picture of the setup operating in our laboratory. . . . . . . . . . 137
8.5
(a) Temporal output of the phase-modulated ARR when deployed external to the DRO. (b) Zoomed temporal output for
maximum modulation depth. . . . . . . . . . . . . . . . . . . . . 139
8.6
(a) Pulse train obtained with increase in modulation depth, at
modulation frequency of ν ± ∆ν. (b) Zoomed 730 ps pulses at
160 MHz repetition rate. (c) Zoomed 450 ps pulses at 80 MHz
repetition rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.7
Temporal output at modulation depth of µ3 =1.83 rads and modulation frequencies of (i) ν − ∆ν 0 , (ii) ν, and (iii) ν + ∆ν 0 . . . . 142
8.8
Spectrum of the cw, and mode-locked signal corresponding to
160 MHz (ν ± ∆ν) and 80 MHz (ν ± ∆ν 0 ) pulses, extracted from
the DRO near degeneracy at T =51.5 o C. . . . . . . . . . . . . . 144
8.9
Spectrum of the cw, and mode-locked signal corresponding to
160 MHz (ν ± ∆ν) and 80 MHz (ν ± ∆ν 0 ) pulses, extracted from
the DRO at T =50 o C. . . . . . . . . . . . . . . . . . . . . . . . 144
8.10 Enhancement of the SHG output for mode-locked operation
with respect to cw operation, detected using a photodetector
for (a) 160 MHz pulses (ν ± ∆ν) and (b) 80 MHz pulses (ν ± ∆ν 0 ).145
8.11 Schematic of the experimental setup. λ/2: Half-wave plate,
PBS: Polarizing beam-splitter, L: Lens, M: Cavity mirrors, OC:
Output coupler; EOM: Electro-optic phase modulator. . . . . . 147
16
List of Figures
8.12 (a) Pulse train obtained at modulation frequency of ν ±∆ν, and
for modulation depths of (i) µ1 (ii) µ2 (iii) µ3 (iv) µ4 and (v)
µ5 . (b) Pulse train obtained at modulation frequency of ν ± ∆ν 0
and for modulation depth of µ3 . Inset: Zoomed 533 ps pulses
at 80 MHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
8.13 Time trace of the mode-locked output at 160 MHz over 15 minutes. Inset: Mode-locked output pulse train at 160 MHz over
20 µs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
8.14 Pulse train at 160 MHz for z 0 =6 cm. Inset: Zoomed 953 ps and
471 ps pulses for (i) z 0 =6 cm and (ii) z 0 =1 cm, respectively. . . 152
8.15 Spectrum of the output extracted from the DRO at T =51.5
o
C, under (a) cw operation, and (b) mode-locked operation at
modulation frequency of ν ± ∆ν and depth of µ3 =1.83 rads. . . 153
8.16 Spectrum of the output extracted from the DRO at T =50 o C,
for modulation depth of µ3 =1.83 rads, and at modulation frequencies of (a) ν ± ∆ν and (b) ν=80 MHz.
. . . . . . . . . . . 154
8.17 Schematic of the experimental setup. λ/2: Half-wave plate,
PBS: Polarizing beam-splitter, L: Lens, M1−5 : Cavity mirrors,
M: Dichroic mirror, EOM: Electro-optic phase modulator. . . . 156
8.18 Idler output pulse train obtained at modulation frequency (ν1 <ν<ν2 )
and modulation depth (µ0 >µ00 >µ000 ) of (i) ν1 , µ0 ; (ii) ν, µ0 ; (iii)
ν2 , µ0 ; (iv) ν, µ00 ; (v) ν, µ000 . . . . . . . . . . . . . . . . . . . . . 158
8.19 (a) Applied modulation, (b) 80 MHz, and (c) 160 MHz repetition rate idler pulses at µ0 =0.18 rads. . . . . . . . . . . . . . . . 159
8.20 Signal pulses at (a) 160 MHz and (b) 80 MHz. . . . . . . . . . . 159
8.21 Spectrum of the mode-locked signal at 160 MHz. . . . . . . . . . 160
List of Figures
17
8.22 Signal pulse train at 80 MHz over 500 µs. . . . . . . . . . . . . . 161
Chapter 1
Introduction
The invention of the laser [1] represents an extraordinary leap in science and
technology. With its tremendous progress in the last few decades, it has now
become omnipresent, catering for various industrial and medical applications,
while also playing important role in different aspects of our life. The unique
property of direct generation and manipulation of coherent light has made the
laser a remarkable tool. The laser is a source that emits light with spectral
purity based on stimulated emission between quantized energy levels in the
laser material. There are many practical applications where high-power coherent light source with high beam quality and, importantly, broad wavelength
tunability is required [2]. To develop a tunable laser, materials with broadened energy levels that result in broad gain spectra can be used. However, the
maximum continuous spectral coverage still remains limited [3]. Figure 1.1
shows the wavelength coverage of some tunable lasers. The most prominent
and widely available tunable laser is the Ti:sapphire laser. It has a broad gain
bandwidth, which is also advantageous for ultrashort pulse generation. The
tunability of the Ti:sapphire laser is, however, limited to at best 300–400 nm.
In addition, even after five decades since the invention of the laser, due to
the restricted availability of suitable gain media, many regions of the optical
20
spectrum extending from the ultraviolet (UV) to the mid-infrared (mid-IR)
remain inaccessible to lasers.
Figure 1.1: Spectral coverage of conventional tunable lasers.
Figure 1.2: Spectral tuning available from OPOs.
The realization of the potential of nonlinear optical phenomena to provide
coherent radiation was indeed a major step in the direction of overcoming
the spectral limitations of lasers [4], as it led to the developement of optical
Chapter 1. Introduction
21
parametric oscillators (OPOs) [5]. OPOs are potentially capable of providing tunable coherent radiation from a single device across extended spectral
regions. Figure 1.2 shows the tuning capability of OPOs. They can also deliver output over the entire temporal spectrum from continuous-wave (cw) to
ultrafast femtosecond time-scales. Such devices are of great interest for a variety of applications from spectroscopy and biomedicine to remote sensing and
environmental monitoring [5].
Nonlinear effects in electromagnetism had indeed been observed long before the invention of laser, in the late 19th century, by John Kerr [6], and later
by Raman in 1927 [7], when he discovered spontaneous scattering of photons
into new frequencies in passing through a transparent medium. The word
nonlinear optics was introduced in 1943 by E. Schrodinger [8, 9]. It was then
in 1961, when the unprecedented optical intensities available from the laser
made the first observation of a coherent nonlinear optical effect possible, as reported by Franken et al. [10], who demonstrated second-harmonic-generation
(SHG) of Ruby laser at 347.2 nm in the quartz crystal. The first observation
of sum-frequency-generation (SFG) was then made by M. Bass in 1962 [11].
However, in order to obtain high conversion efficiencies in nonlinear optical
processes, phase-matching condition needs to be satisfied, which means that
a proper phase relationship needs to be maintained between the interacting
waves along the propagation direction. With the phase-matching condition
satisfied, in the same year of 1962, J. A. Giordmaine demonstrated the first
experiment on the generation of intense SHG, by matching the phase velocities
of the fundamental and the second-harmonic light [12], and later in 1963, Smith
and Braslau demonstrated the first difference-frequency-generation (DFG) [13].
During the same period, the importance of parametric generation and amplification was recognized as an important technique for the generation of tunable coherent radiation in new spectral regions [14–16]. In 1965, Wang and
Racette demonstrated DFG accompanied with the measurement of paramet-
22
ric gain [17]. This process of DFG then corroborated the optical parametric
generation. In the same year, the first experimental demonstration of an OPO
was reported by Giordmaine and Miller [18]. The pump wavelength used in
the experiment was at 529 nm, obtained by the second-harmonic-generation
of a pulse Nd+3 :CaWO4 laser, and the OPO was tunable from 970 nm to 1150
nm. The pulsed OPO was then followed by the demonstration of cw OPOs,
independently by Smith et al. [19] and Byer et al. [20] in 1968. Although, since
these early days, the basic principles behind the optical parametric generation
have been known, due to the unavailability of suitable pump lasers and proper
nonlinear optical materials, the extension of these techniques to shorter time
domains of picoseconds and femtoseconds were not possible for another 20
years.
In the 1980s, the advent of new nonlinear optical materials and new laser
sources with improved spatial and spectral coherence and sufficient intensity
in the desired spectral regions once again prompted a major resurgence of
interest in the development of pulsed OPOs [21–24]. This then led to the
first demonstration of a synchronously-pumped femtosecond OPO by D. C.
Edelstein in 1989 [25]. Today, with the tremendous progress in the field, there
are numerous pulsed OPOs in the spectral regions from the mid-IR [2, 26] to
the visible [27], and further down to the UV [28], using nonlinear crystals such
as LiB3 O5 (LBO), β-BaB2 O4 (BBO) and BiB3 O6 (BIBO). The generation of
terahertz radiation from pulsed OPOs has also been demonstrated [29].
Due to the substantially lower nonlinear gain available under cw pumping, cw OPOs have been traditionally the more challenging class of devices.
The spectrally pure, high-power and tunable cw OPO are of great importance for numerous applications. A high-power (watt-level) pump laser, optical material with high nonlinearity, and lower oscillation threshold pump
power are typical requirements for successful operation of cw OPOs. The
singly-resonant oscillator (SRO) configuration of a cw OPO, where a single
Chapter 1. Introduction
23
wave (signal or idler) resonates inside the OPO cavity, despite having high
operation threshold power, are advantageous for the generation of high-power
single-frequency radiation over extended spectral regions. The first cw SRO
was demonstrated by Yang et al. in 1993 using birefringent KTP crystal [30],
utilizing type II noncritical phase-matching. To overcome the high cw SRO
threshold, various techniques based on different resonance configurations have
also been deployed, which include doubly-resonant oscillator (DRO), triplyresonant oscillator (TRO), pump-enhanced SRO (PE-SRO) and intracavity
SRO (IC-SRO) [31–34]. The advent of quasi-phase-matching technology based
on periodical poling of nonlinear materials in 1991 [35], had a major impact
on the development of high-power cw OPOs. In 1996, Bosenberg at al. [36]
demonstrated the first cw OPO based on periodically-poled LiNbO3 (PPLN).
Since then, the development of novel quasi-phase-matched (QPM) materials,
new innovations in resonance configurations and improved pumping techniques
using stable, high-power laser sources have led to important breakthroughs in
cw OPOs [37–41].
A majority of cw OPOs developed till date are based on PPLN [36–39,
41–43]. The high effective nonlinearity (d ef f ∼17 pm/V) and long interaction
length available with PPLN crystal has brought the threshold of cw SROs well
within the reach of available cw lasers. It has enabled the cw SRO operation at
unprecedented power levels, high conversion efficiencies, and providing spectral
coverage from 1 µm to 5 µm [38, 41–43]. To prevent the PPLN crystal from
photorefractive damage, the crystal is doped with MgO, then well-known as
MgO:PPLN. On the other hand, MgO-doped periodically-poled stoichiometric
LiTaO3 (MgO:sPPLT), due to its increased resistance to photo-refractive damage and moderate nonlinear coefficient (d ef f ∼9 pm/V ), is a promising material
in the UV to near-infrared (near-IR) regions, especially in high-power operation [40,44]. The attainment of first-order quasi-phase-matching for the generation of UV output is, however, challenging till date. To increase the extraction
24
Figure 1.3: Approach of the thesis research work.
Chapter 1. Introduction
25
efficiency and wavelength tunability of cw SROs, various techniques such as
output coupling and intracavity SHG have also been employed [41, 45, 46].
The advent of these QPM nonlinear crystals has also enabled the direct active
mode-locking of cw OPOs, generating steady-state pulses [47].
The approach of the research work presented in this thesis is shown in
Fig. 1.3. The work performed was purely under cw pumping, using three
commercial, narrow-linewidth, linearly-polarized, cw laser sources. Using a
compact fiber laser at 1940 nm, efficient single-pass SHG at 970 nm, has been
demonstrated and investigated. Another fiber laser at 1064 nm has been used
to pump a cw SRO based on MgO:PPLN. The cw SRO, tunable in the mid-IR
range, has been interferometrically output-coupled, providing continuous and
fine control of output-coupling optimization. To extend the emission into nearIR range, the intracavity signal has been frequency-doubled using a fanoutgrating MgO:sPPLT. To generate output in the UV, down to 355 nm, sumfrequency-mixing of the second-harmonic output of the fiber laser and the
pump at 1064 nm has been performed in BIBO. The solid-state laser in the
green has been used to demonstrate a dual-wavelength OPO. The cw OPOs,
both in DRO as well as in SRO configuration, pumped in the green, and based
on MgO:sPPLT, are further actively mode-locked to generate stable picosecond
pulses. The thesis is organized into 9 chapters.
Chapter 2 provides an introduction to nonlinear optics and various nonlinear
optical phenomena, including SHG, SFG, DFG and OPO. The wavelength
tuning capabilities of an OPO have been discussed. Since a proper cavity
design is required for successful operation of a cw OPO, we have discussed the
design issues. The phenomenon of active mode-locking method that can be
employed in cw OPOs have also been presented in this chapter.
Out of the different viable methods for SHG that have relied on intracavity,
external resonant enhancement, and multiple-pass configurations, the external
26
single-pass SHG (SP-SHG) is the simplest approach. The combination of a
cw fiber laser and SP-SHG based on a periodically-poled nonlinear crystal
is a potential approach for high-power generation, not only because of its
compact and practical design, but also due to the high spatial beam quality
and narrow linewidth, which is inherently transfered from the fiber laser to
the second-harmonic output. We demonstrate such a high-power, fiber-laserbased, linearly-polarized, cw source at 970 nm in chapter 3. Also relevant
theoretical studies for the characterization of SP-SHG in the crystal have been
performed and presented in this chapter.
In chapter 4, we demonstrate the successful deployment of an antiresonant
ring (ARR) interferometer for the attainment of optimum output coupling in
a cw OPO. The cw OPO, configured as a SRO, and pumped at 1064 nm,
is based on MgO:PPLN crystal, with the ARR interferometer integrated into
one arm of the standing-wave cavity. The proof-of-principle demonstration
confirms the effectiveness of the technique for continuous, in situ, and fine
control of output coupling in cw OPOs to achieve maximum output power
at any arbitrary pumping level above threshold. The theoretical calculations
performed for conventional output-coupled cw SRO are also presented in this
chapter.
In chapter 5, a high-power, single-frequency, cw source tunable across 775807 nm in the near-infrared, based on internal SHG of a cw SRO, pumped
at 1064 nm, is demonstrated.
The compact, all-periodically-poled source
employs multigrating MgO:PPLN crystal for the OPO and a fanout-grating
MgO:sPPLT crystal for intracavity SHG. The cw SRO is further tunable across
3125-3396 nm in the idler, providing high output power. The results of output
power across the tuning range, power scaling, power stability, beam quality
and linewidth measurement are presented in this chapter.
Using the cw Yb-fiber laser at 1064 nm and the second-harmonic output
Chapter 1. Introduction
27
of the pump, we performed sum-frequency-mixing in BIBO. We have demonstrated the generation of cw UV output at 354.7 nm in single-pass configuration. The results of power scaling, power stability, frequency stability, and
beam quality are presented in chapter 6.
In chapter 7, we demonstrate two cw OPOs coupled together with an ARR
interferometer, generating two pairs of signal and idler wavelengths. The
OPOs, configured as SROs, based on identical 30-mm-long MgO:sPPLT crystals, are pumped by a single cw laser at 532 nm. The two pairs of signal and
idler wavelengths can be independently and arbitrarily tuned to indefinitely
close spacing, through degeneracy, and beyond, across the wavelength range of
870-1370 nm. The closest frequency separation and power scaling results are
also presented in this chapter.
In chapter 8, the green-pumped cw OPO is then further demonstrated to
generate mode-locked pulses. The generation of picosecond pulses is demonstrated in both DRO as well as SRO configuration. A mode-locking technique
based on the deployment of a phase modulator in combination with an ARR
interferometer internal to a cw DRO, providing phase-to-amplitude modulation, has been presented. The direct active mode-locking of the DRO based on
pure phase-modulation using the phase modulator as the single mode-locking
element is then demonstrated. Further, direct phase-modulation mode-locking
of a cw OPO in SRO configuration has been achieved. The OPOs, pumped at
532 nm, are based on MgO:sPPLT as the nonlinear gain crystal. The results of
record picosecond pulse duration, effect of intracavity frequency detuning and
change in modulation depth on the pulse duration and repetition rate have
been investigated. The output spectrum and the confirmation of mode-locked
operation have also been presented in this chapter. Finally, in chapter 9 the
thesis has been concluded with some of our ongoing effort and future outlook
in the field.
Chapter 2
Basics of nonlinear optics
2.1
The origin of optical nonlinearity
Optics is the study of interaction of electromagnetic radiation with matter.
When an electromagnetic wave interacts with a dielectric material, the electrons are displaced with respect to the nuclei, and it induces a polarization,
defined as dipole moment per unit volume. The dipole oscillations in a dielectric material can result in the emission of light waves. The energy and
wavelength of the light wave so generated is determined by the dipole moment
and dipole oscillation frequency [48, 49]. When the magnitude of the input
electric field is small, the induced polarization follows a linear dependence on
the input field strength,
P = 0 χ(1) E
(2.1)
where P and E are the polarization and electric field vectors, respectively, χ(1)
is the linear susceptibility of the medium, and 0 is the permittivity of free
space. This is the regime of linear optics, where the dipole oscillation and the
emitted optical wave from the dipole are at the same frequency as the input
field. On the other hand, if the field strength is strong enough, the dipole
displacement becomes nonlinear with the electric field. This is the regime of
30
2.2. Second-order nonlinear susceptibility
nonlinear optics, where the dipole oscillates not only at the input frequency,
but also above and below the input frequency, generating new wavelengths. In
such case, the induced polarization, P, in its most general form is given by
P = 0 (χ(1) E + χ(2) E 2 + χ(3) E 3 + .....)
(2.2)
where χ(2) , χ(3) ,..... are the higher-order nonlinear susceptibilities. The crystalline media that exhibit even-order nonlinearity are non-centrosymmetric
materials, whereas for odd-order nonlinearity, centrosymmetric as well as noncentrosymmetric materials can be used. For the attainment of such optical
nonlinearity, higher optical intensities are required, which can be provided
only by a laser. Nonlinear optics is a vast field that involves the study of
various nonlinear optical interactions. The work demonstrated in this thesis
is based on second-order nonlinear processes. As such, the brief discussion on
nonlinear processes given here will be limited to interactions that involve the
second-order nonlinear susceptibility, χ(2) . Description of other interactions
can be found in a multitude of references [4, 48, 50].
2.2
Second-order nonlinear susceptibility
The second-order nonlinear optical interactions can be described in terms of
the nonlinear polarization given by
P N L = 0 χ(2) E 2
(2.3)
(2)
where the second-order nonlinear susceptibility, χ(2) = χijk , is a tensor of
rank 3. The indices i, j, k refer to the Cartesian components of the field and
represent the polarization directions. The d-tensor notation, which is used
when the Kleinman symmetry condition is valid, is given by [48, 50]
1 (2)
dijk = χijk .
2
(2.4)
Chapter 2. Basics of nonlinear optics
31
Under the Kleinman symmetry condition, where frequencies of the interacting waves are far from the resonance frequency of the material, the nonlinear
susceptibility is essentially independent of frequency, and the indices can be
permuted without permuting the frequencies. The nonlinear susceptibility tensor can then be contracted into a 3x6 matrix, and the nonlinear polarization
is described by




d11

 
P  = 20 K d
 21
 y

 
 Px 
d12 d13 d14 d15
d22 d23 d24 d25
d31 d32 d33 d34 d35
Pz
Ex2







2

Ey



d16  

2


Ez




d26  


 Ey E z + Ez Ey 


d36 

 Ex E z + Ez Ex 




(2.5)
Ex E y + Ey Ex
where K is the degeneracy factor, whose value depends on the conversion
processes.
2.3
Second-order nonlinear optical interactions
If we consider an optical field consisting of two distinct frequency components,
ω1 and ω2 , incident upon a nonlinear medium, which can be represented by
E(t) = E1 (t)e−iω1 t + E2 (t)e−iω2 t + c.c.
(2.6)
then using equations 2.3 and 2.6, the second-order nonlinear polarization is
given by
P NL =
X
P (ωn )e−iωn t = 0 χ(2) [E12 e−2iω1 t + E22 e−2iω2 t + 2E1 E2 e−i(ω1 +ω2 )t
n
+ 2E1 E2∗ e−i(ω1 −ω2 )t + c.c.] + 20 χ(2) [E1 E1∗ + E2 E2∗ ] (2.7)
where the first two terms on the right-hand-side represent the second-harmonicgeneration (SHG) process, the third and fourth term represents the sumfrequency-generation (SFG) and difference-frequency-generation (DFG) processes, respectively, and the last term is known as optical rectification (OR).
32
2.3. Second-order nonlinear optical interactions
It is to be noted that the degenaracy factor, K , described in section 2.2, takes
the value of 1/2 for SHG and optical rectification, and 1 for the other conversion processes.
Figure 2.1: Schematic of various second-order nonlinear processes. (a) SFG, (b) SHG, (c)
DFG, (d) OPG, and (e) OPO.
The physical meaning of these second-order nonlinear frequency conversion
processes are illustrated using the photon picture in Fig. 2.1. In SFG process,
as shown in Fig. 2.1(a), two low-energy pump photons at frequencies ω1 and
ω2 , are combined to generate one higher-energy photon at frequency, ω3 =
ω1 + ω2 . The SHG is the degenerate case of SFG process, where two lowenergy pump photons at same frequency, ω1 = ω2 = ω, are combined to
generate one photon of energy twice that of the pump photon energy, and at
frequency ω3 = 2ω, as shown in Fig. 2.1(b). Another special case that has
Chapter 2. Basics of nonlinear optics
33
found important applications is when ω1 =0 and ω3 = ω2 = ω. Then, one of the
input fields is static, and the refractive index of the medium is affected through
the linear electro-optic effect. This is also known as the Pockels effect. In DFG
process, two pump photons of frequency, ω1 and ω3 , are combined to generate
one photon at difference frequency of ω2 = ω1 − ω3 , as shown in Fig. 2.1(c). A
special case, when the two pump photons have the same frequency, ω, resulting
in ω2 = 0, leads to optical rectification, where a static electric field is created
within the nonlinear medium. Figure. 2.1(d) shows another type of process
known as parametric down-conversion or optical parametric generation (OPG),
where spontaneous break-down of high-energy pump photon at frequency, ω3 ,
into two constituent low-energy photons at frequencies, ω1 and ω2 , occurs. The
two generated wavelengths are referred to as the signal and the idler, of which
the signal is, generally, the one with the shorter wavelength. For practical
realization of the parametric process and to obtain macroscopic output, the
nonlinear medium is enclosed within an optical resonator, and the device is
then called optical parametric oscillator (OPO), as shown in Fig. 2.1(e).
2.4
Coupled-wave equations for second-order nonlinear
processes
The previous sections of this chapter have shown the response of a nonlinear
medium to intense optical field, that induces nonlinear polarization, resulting
in the generation of new frequency components. The interaction between the
involved fields can be described by Maxwell’s wave equations [48].
For a nonlinear, non-magnetic optical medium that contain no free charges
and no free currents, the optical wave equation for the propagation of electromagnetic radiation through this medium can be represented by
∇2 E −
1 ∂ 2P
1 ∂ 2E
=
c2 ∂t2
0 c2 ∂t2
(2.8)
34
2.4. Coupled-wave equations for second-order nonlinear processes
√
where c=1/ µ0 0 is the speed of light in vacuum, and µ0 is the permeability
of free space.
In a lossless nonlinear medium, the optical field at a frequency, ωj , where
j=1,2,3 represent the three interacting fields propagating in the z direction, is
given by
Ej (z, t) = E(z, ωj )ei(kj z−ωj t) + c.c.
(2.9)
and the nonlinear source term is given by
Pj (z, t) = P (z, ωj )ei(kj z−ωj t) + c.c.
(2.10)
where k j is the wavenumber expressed as
kj =
nj (ωj )ωj
c
(2.11)
with refractive index, n j represented as
s
nj =
(ωj )
0
(2.12)
where is the permittivity of the medium at frequency, ωj . In the above
expressions, we have assumed that the amplitudes of the fields vary slowly over
a distance comparable to the wavelength, known as slowly-varying amplitude
approximation and is valid whenever [48],
dE d 2 Ej
j
kj
.
2
dz
dz (2.13)
Using equations 2.3, 2.9, 2.10 and 2.13, the wave equation for each field
involved becomes
∂E1
iω 2 def f
= 1 2 E3 E2∗ ei∆kz
∂z
k1 c
(2.14)
∂E2
iω22 def f
=
E3 E1∗ ei∆kz
2
∂z
k2 c
(2.15)
∂E3
iω 2 def f
= 3 2 E1 E2 e−i∆kz
∂z
k3 c
(2.16)
Chapter 2. Basics of nonlinear optics
35
where d ef f is the effective nonlinear coefficient, and ∆k = k3 − k2 − k1 is
called the wavevector mismatch or phase-mismatch. The effective nonlinear
coefficient and the wavevector mismatch, both depend on material properties,
propagation direction, and the optical frequencies. Equations 2.14, 2.15 and
2.16 are called coupled-amplitude equations, where various frequency components are coupled by the nonlinear interaction. It shows the variation in the
amplitude of one field due to its coupling to the other fields.
2.5
Phase-matching
For the attainment of an efficient nonlinear conversion process, two conditions
need to be satisfied. One is the energy conservation, where the interacting
waves obey the frequency relation, ω3 = ω1 + ω2 , and the second is the phasematching between the optical fields, given by ∆k = k3 − k2 − k1 = 0. A
perfect phase-matching, where ∆k = 0, is the ideal case. In classical picture,
at perfect phase matching, the individual dipoles in the medium are properly
phased, resulting in the addition of the field emitted by each dipole in the
forward direction. The field amplitude grows linearly with the propagation
distance, as shown in Fig. 2.2(a). However, in general, as the optical waves at
different frequencies propagate with different phase velocities, because of the
dispersion in the nonlinear medium, ∆k 6= 0. Because of this, after travelling a
short distance known as the coherence length, lc = 2π/∆k, the relative phase
of the interacting waves slips by 180o . Along the propagation direction in the
nonlinear medium, the waves step in and out of phase periodically, resulting in
exchange of energy back and forth. This periodic oscillation along the propagation direction is illustrated as the phase-mismatch or non-phase-matched curve
in Fig. 2.2(b). There are two important techniques to achieve phase-matching,
birefringent phase-matching (BPM) and quasi-phase-matching (QPM).
36
2.5. Phase-matching
Figure 2.2: Generated wave intensity as a function of propagation distance in nonlinear
crystal for (a) perfectly phase-matched (∆k = 0), (b) non-phase-matched (∆k 6= 0), and (c)
quasi-phase-matched conditions.
2.5.1
Birefringent phase-matching
The most common technique for achieving phase-matching is the birefringent
phase-matching (BPM), where the birefringence of a nonlinear crystal is exploited. Birefringence is the property of some anisotropic optical materials,
where the refractive index of the material depends on the polarization and
propagation direction of light. When the interacting waves of different frequencies are polarized differently, their corresponding phase velocities can be
adjusted, so that the index difference due to dispersion is balanced by the
index difference due to birefringence.
Depending upon the number of optic axes, a birefringent crystal can be
divided onto two categories, uniaxial (one optic axis) and biaxial crystals (two
optic axes) [50, 51]. In a uniaxial crystal, the light beam whose polarization is
normal to the optic axis is called an ordinary beam or o-beam, and the beam
polarized in the optic axis plane is known as extraordinary beam or e-beam.
The refractive index of the o-beam, n o , does not depend on the propagation
Chapter 2. Basics of nonlinear optics
37
direction, whereas the refractive index of the e-beam, n e , does. If θ is the angle
between propagation direction and the optic axis, then the refractive index of
the e-beam as a function of θ is given by
cos2 (θ) sin2 (θ)
1
=
+
n2e (θ)
n2o
n2e
(2.17)
The difference, ∆n(θ) = ne (θ) − no , determines the birefringence of the material. Thus, the following equations are evident:
ne (θ = 0o ) = no
(2.18)
ne (θ = 90o ) = ne
(2.19)
∆n(θ = 0o ) = 0
(2.20)
∆n(θ = 90o ) = ne − no
(2.21)
The crystal has positive or negative birefringence, if n o <n e or n o >n e , respectively, as illustrated in Fig. 2.3. The BPM can be realized in two types,
Type I and Type I. In Type I, the driving fields have the same polarization
and the generated field is orthogonally polarized compared to the driving field.
In Type II, the driving fields are orthogonally polarized. To understand BPM,
we consider SHG process in a positive uniaxial crystal with Type-I phasematching. Figure 2.4 shows the propagation direction at an angle θ, where
the extraordinary index for the fundamental wave at frequency, ω, is equal
to the ordinary index for the second-harmonic wave at frequency, 2ω, thus
compensating the dispersion and resulting in perfect phase-matching.
Depending upon the value of θ, BPM can also be catogorized into critical phase-matching, CPM (θ 6= 90o ), and noncritical phase-matching, NCPM
(θ = 90o ). In CPM, the refractive index, n e , and the phase velocity become
dependent on angle, θ, leading to a reduction in the spatial overlap between
the interacting ordinary and extraordinary polarized waves in the nonlinear
crystal, thus limiting the interaction length of the nonlinear material. This
38
2.5. Phase-matching
Figure 2.3: Index ellipsoids for (a) positive uniaxial crystals and (b) negative uniaxial crystals.
Figure 2.4: Illustration of birefringent phase-matching for SHG in uniaxial crystal.
Chapter 2. Basics of nonlinear optics
39
phenomenon is known as spatial walk-off or Poynting vector walk-off. The
spatial walk-off angle, ρ, can be represented as
tan(ρ) = −
1 dne (θ)
ne (θ) dθ
(2.22)
In a biaxial crystal, the propagation direction of the wave is defined by
two angles, polar (θ) and azimuthal (φ). For simplicity, it is conventional to
consider the wave propagation in the xy, yz and xz principal planes. The two
optic axes are taken to lie in the xz plane, and these make an angle, Ω, with
the z-axis, as illustrated in Fig. 2.5.
Figure 2.5: Schematic of wave propagation for biaxial crystal, in the crystal coordinate
system.
The propagating wave is at angle θ with respect to the z-axis, and at φ
with respect to the x-axis. In xy plane, θ = 90o , and φ varies from 0o to
90o , whereas in yz plane, φ = 90o , and θ varies from 0o to 90o . Considering
nx < ny < nz , where n x , n y and n z are the principal values of the refractive
indices, in xy plane,
no = nz
(2.23)
40
2.5. Phase-matching
ne (φ) =
ny (1 + tan2 φ)1/2
[1 + (ny /nx )2 tan2 φ]1/2
(2.24)
and in yz plane,
no = nx
ne (θ) =
2.5.2
ny (1 + tan2 θ)1/2
[1 + (ny /nz )2 tan2 θ]1/2
(2.25)
(2.26)
Quasi-phase-matching
There are circumstances when the BPM technique, described in the previous
section, are not suitable, such as when the material does not possess sufficient
birefringence to compensate for the refractive index difference due to dispersion, or when a particular application requires nonlinear coefficient much larger
than the off-diagonal tensor elements. Under these situations, an alternative
technique know as quasi-phase-matching (QPM) can be used. Armstrong et
al. were the first to suggest the QPM technique [4]. Unlike BPM, QPM is not
perfect phase-matching. The idea of QPM is illustrated in Fig. 2.6(a). In the
nonlinear crystal, after each coherence length, l c , the sign of all the components
of nonlinear susceptibility tensor is reversed. Thus, the polarization is shifted
by 180o after each coherence length, making the interacting waves propagate
in phase along the propagation direction. The introduction of the additional
phase is realized by modulating the nonlinear coefficient of the medium with a
period Λ = 2lc . The nature of this effect has been illustrated in Fig. 2.2(c). As
evident, the build-up of output intensity is less rapid than that in the case of
perfect phase-matching. Hence, QPM can result in lower conversion efficiency
as the nonlinear coefficient is given by
dm =
2
def f
mπ
(2.27)
where m is referred as order of the QPM. However, QPM permits the use of
the same polarization direction for all interacting waves, accessing the highest
diagonal coefficients of the nonlinear tensor. As such, the conversion efficiency
Chapter 2. Basics of nonlinear optics
41
Figure 2.6: (a) Periodic inversion of the sign of the nonlinear coefficient, and (b) fanout
grating structure, in a QPM nonlinear material.
in case of QPM technique can be significantly higher than that by BPM technique. Moreover, using NCPM configuration, the spatial walk-off between the
interacting fields can be avoided. The most popular technique to fabricate
quasi-phase-matched crystals is periodic reversal of the domains of ferroelectric materials such as LiNbO3 and LiTaO3 . By applying a strong periodic
electric field, the spontaneous electronic polarization of these materials can
be inverted. This technique is known as periodic poling. The advancement
in periodic poling technology also allows the fabrication of crystals in fanout
grating structures, as shown in Fig. 2.6(b).
2.6
Second-harmonic and sum-frequency-generation
As shown in Fig. 2.1(a), sum-frequency-generation is the process where two
photons at frequencies, ω1 and ω2 , interact to generate an output photon at a
frequency, ω3 . If the two input photons are at same frequency, ω, the output
frequency is at the second-harmonic, 2ω, as illustrated in Fig. 2.1(b). For
42
2.6. Second-harmonic and sum-frequency-generation
an efficient nonlinear process, optimum crystal length, and broad spectral and
temperature acceptence bandwidths are important criteria [50, 52]. For the
SHG process, the spectral acceptance bandwidth is given by
0.4429λω
∆λω =
l
−1
n − n
∂nω 1 ∂n2ω ω
2ω
+
−
λω
∂λω 2 ∂λω (2.28)
where λω is the pump or fundamental wavelength, l is the length of the nonlinear crystal, n ω and n 2ω are the refractive indices of the fundamental and the
generated second-harmonic wave, respectively. The temperature acceptance
bandwidth can be given by
−1
0.4429λω n2ω − nω
+
α(n
−
n
)
∆T =
2ω
ω l
∂T
(2.29)
where α is the linear thermal expansion coefficient of the nonlinear crystal.
For SHG, the conversion efficiency under plane-wave and undepleted pump
approximation is given by
ηSHG
P2ω (l)
∆kl
o
=
= ηSHG
sinc2
Pω (0)
2
o
ηSHG
!
(2.30)
8π 2 d2ef f l2 Iω
=
0 n2ω n2ω cλ2ω
where P ω is the fundamental power, P 2ω is the SHG power, and I ω is the fundamental intensity. The phase-matching condition in the case of periodicallypoled materials is attained by,
∆k = k2ω − kω −
2π
Λ
(2.31)
The SFG process exhibit similar behaviour, with the conversion efficiency
under similar approximations represented as
Chapter 2. Basics of nonlinear optics
ηSF G
Pω3 (l)
o
2 ∆kl
=
= ηSF
G sinc
Pω1 (0)
2
o
ηSF
G
43
!
(2.32)
8π 2 d2ef f l2 Iω2
=
0 nω1 nω2 nω3 cλ2ω3
where P ω1 and I ω1 are the fundamental power and the fundamental intensity,
respectively, P ω3 is the SFG power at SFG wavelength of λω3 , and n ω1 , n ω2
and n ω3 are the refractive indices of the interacting waves at frequencies ω1 ,
ω2 and ω3 , respectively.
2.7
Optical parametric oscillator
As illustrated in Fig. 2.1(e), an optical parametric oscillator (OPO) essentially consists of a nonlinear medium enclosed by an optical resonator. It is a
device based on three-wave interaction process, where a nonlinear material is
pumped by an intense input pump field, to generate signal and idler output
at macroscopic level, while satisfying energy conservation and phase-matching
conditions [49, 53]. The signal and idler are initially generated by the process
of parametric noise that corresponds to the spontaneous optical parametric
generation. For attaining macroscopic amplification of the generated waves,
positive feedback is necessary, that requires an optical oscillator. Thus, as in
lasers, OPOs are operated in an oscillator configuration. The primary difference between the lasers and OPOs is that the optical gain in OPOs comes from
the parametric amplification in the nonlinear crystal and not from the stimulated emission of population inversion. Unlike the laser, in the OPO there is
no energy storage and the gain is only available in the presence of pump.
2.7.1
Parametric gain and amplification
Under phase-matching condition, the parametric noise is amplified during the
44
2.7. Optical parametric oscillator
propagation through the medium. The single-pass parametric gain in the nonlinear crystal is given by
Gs (L) =
sinh2 [Γ2 l2 − ( ∆kl
)2 ]1/2
Is (l)
2
− 1 = Γ2 l2
Is (0)
)2 ]
[Γ2 l2 − ( ∆kl
2
(2.33)
where I s is the signal field intensity, and Γ is the gain factor defined as
8π 2 d2ef f
Γ =
Ip (0)
c0 np ns ni λs λi
2
(2.34)
Here, I p is the pump intensity, and n p , n s and n i are the refractive indices
of the pump, signal and idler at wavelengths λp , λs and λi , respectively. At
degeneracy, when, λi = λs = 2λp , the gain factor can also be expressed in the
form
Γ2 =
8π 2 d2ef f
(1 − δ 2 )Ip (0)
c0 np n20 λ20
(2.35)
where λ0 = 2λp is the degenerate wavelength, n 0 is the refractive index at
degeneracy, assuming n0 ∼ ns ∼ ni , and δ is the degeneracy factor. The
parametric gain is maximum when, δ ∼ 0, and the gain decreases for operation
away from degeneracy as δ → 1.
Under perfect phase-matching condition, by setting ∆k = 0 in equation
2.33, the net single-pass signal gain reduces to
Gs (l) = sinh2 (Γl)
(2.36)
which, for low gains (Γl . 1), approximates to
Gs (l) ∼
= Γ2 l 2
(2.37)
and for high gains (Γl 1), reduces to
1
Gs (l) ∼
= e2Γl
4
(2.38)
Chapter 2. Basics of nonlinear optics
45
Hence, under the phase-matching condition, the single-pass signal gain has a
quadratic dependence on Γ in the low-gain limit, whereas it increases exponentially with 2Γ in the high-gain limit.
2.7.2
Oscillator configurations
The losses in an OPO cavity primarily originate from the limited reflections of
the cavity mirrors, in addition to the losses due to scattering, and absorption
in the crystal. As such, while extracting the wave(s) of interest, the other
waves are resonated inside the optical cavity. Depending on the number of
waves resonating in the optical cavity, there are four major configurations, as
illustrated in Fig. 2.7. In singly-resonant oscillator (SRO), one of the generated
wave (signal or idler) is resonated, while the other is completely extracted from
the cavity together with the undepleted pump. The doubly-resonant oscillator
(DRO) resonates both the signal and idler, while the undepleted pump is
extracted. In triply-resonant oscillator (TRO), all three waves are resonated.
To enhance the pump in the cavity, another configuration known as pumpenhanced SRO (PE-SRO) is used, where one of the generated waves together
with the pump is resonated inside the cavity.
The advantage of DROs, particularly in continuous-wave operation, where
the pump intensity is low, is that the oscillation threshold pump power can
be much lower as compared to that in the SRO. On the other hand, in spite
of the high operation threshold of SROs, they provide single-frequency output
with stable performance.
2.7.3
Steady-state threshold in cw OPOs
The determination of the oscillation threshold pump power, particularly under
continuous-wave pumping, is an important factor. Considering plane-wave and
46
2.7. Optical parametric oscillator
Figure 2.7: Cavity configurations for OPOs: (a) singly-resonant (SRO), (b) doubly-resonant
(DRO), (c) triply-resonant (TRO), and (d) pump-enhanced (PE-SRO).
undepleted pump approximation, and assuming phase-matched interaction and
single-pass of the pump, the threshold in SRO and DRO are presented here.
Singly-resonant oscillator
Considering the signal as the resonating wave, the pump intensity required to
reach the oscillation threshold can be expresed as
Ith =
αs c0 np ns ni λs λi
8π 2 l2 d2ef f
(2.39)
where αs is the fractional round-trip power loss in the SRO for the signal wave.
Doubly-resonant oscillator
For DRO, the threshold pump intensity can be expressed as
Chapter 2. Basics of nonlinear optics
Ith =
47
αs c0 np ns ni λs λi αi
8π 2 l2 d2ef f
4
(2.40)
where αs and αi are the round-trip power loss of signal and idler wave, respectively, in the DRO cavity. The threshold of the DRO is reduced by a factor of
(αi /4) as compared to the SRO.
2.7.4
Wavelength tuning
The OPOs are well-known for their wide wavelength tunability. Under phasematched condition, ∆k∼0, the phase-matching relation reduces to
np ns ni
2π
−
−
λp λs λi
!
=0
(2.41)
Thus, the wavelength tuning can be attained by changing any of the physical
parameter that influences the refractive index of the nonlinear medium, while
maintaining the phase-matched condition. The common parameters that are
used are:
• Crystal angle (Angle tuning)
• Crystal temperature (Temperature tuning)
• Pump wavelength (Pump tuning)
For periodically-poled crystals, the quasi-phase-matched grating periods (Grating tuning) can also be used for tuning. Figure 2.8 shows typical wavelength
tuning curves for a MgO:PPLN-based SRO, theoretically calculated from the
relevent Sellmeier equations [54], where crystal temperature and the grating
period are varied.
48
2.8. Nonlinear materials
Figure 2.8:
The tuning curves for signal and idler wavelengths for a 1-µm-pumped
MgO:PPLN OPO.
2.8
Nonlinear materials
There are several important parameters that have to be taken into consideration when selecting a nonlinear crystal for developing an efficient frequency conversion source. For an OPO, the material of choice should be non-centrosymmetric,
should have a broad transparency range at operating wavelengths, large nonlinearity, low spatial walk-off, a high optical damage threshold, good mechanical,
chemical and thermal properties, phase-matching possibility in the wavelength
range of interest, and availability in high optical quality, large size, and at a
low cost. The nonlinear figure-of-merit, reperesented as
F OM = √
def f
np ns ni
(2.42)
is another important factor, as it contains the physical parameters that are
completely dependent upon the material. The larger the FOM , the better the
material. For efficient transfer of energy to the generated waves, it is required
Chapter 2. Basics of nonlinear optics
49
that the material has a broad parametric gain bandwidth. The sinc 2 function
describes the gain lineshape of the parametric medium, and the gain bandwidth
of the nonlinear medium is defined by |∆kl| ∼
= 2π. The spectral (∆λp ), angular
(∆θ) and temperature (∆T ) acceptance bandwidths are also the important
parameters, as they indicates the maximum allowable pump linewidth, angular
divergence and variation in temperature for efficient parametric generation [49].
The acceptance bandwidths are inversely proportional to the crystal length (l).
This implies that shorter crystal lengths can tolerate larger deviations. For
the attainment of maximum parametric gain and minimum OPO threshold,
the use of nonlinear materials with large spectral, angular, and temperature
acceptance bandwidths is advantageous.
Using a Yb-fiber laser at 1064 nm as the pump source, we performed SHG
to generate output at 532 nm, in LiTaO3 and LiNbO3 crystals, in congruent
and stoichiometric compositions, provided by HC photonics. The crystals are
of equal lengths, l=10 mm. The pump beam was focussed at the centre of the
crystals to beam waist radii of 32 µm, and the maximum available pump power,
P ω , was 27.8 W. Table 2.1 shows the various parameters of these nonlinear
crystals, obtained from the measurements.
For a birefringent material under CPM condition, another factor to be considered is the spatial walk-off. The effective interaction length in the presence
of walk-off is given by
lef f
√
πωp
=
ρ
(2.43)
The effective length of the crystal can be increased by increasing the pump
beam waist radius. However, efficient nonlinear optical processes require high
pump intensity, and hence the pump beam waist needs to be well focused. As
such, to achieve practical efficiencies, a good balance between the crystal length
and beam radii must be maintained. Also, spatial walk-off can be overcome
by using NCPM (θ = 90o ).
power (W)
2.58
2.97
2.83
1.60
0.219
2.42
crystal
VTE-SLT
SLT
SLT
MCLT
VTE-CLT
SLN
10.84
0.78
5.75
10.23
10.69
9.37
(%)
efficiency
Max. SHG
2.63
–
3.53
3.51
3.63
1.52
3.2
3.06
3.46
3.63
3.04
Pω =27.8 o C
Pω =9 o C
3.49
∆T (o C) @
∆T (o C) @
-0.165
-0.120
-0.205
-0.035
-0.033
9.78
1.80
5.63
6.68
6.87
6.50
(pm/V)
(o C/W)
-0.233
def f
dT/dPω
LiTaO3 , MCLT: MgO-doped congruent LiTaO3 , VTE-CLT: Vapor transport equilibration congruent LiTaO3 , SLN: Stoichiometric LiNbO3 .
Table 2.1: Characterization of some nonlinear crystals. VTE-SLT: Vapor transport equilibration stoichiometric LiTaO3 , SLT: Stoichiometric
Max. SHG
Nonlinear
50
2.8. Nonlinear materials
Chapter 2. Basics of nonlinear optics
2.9
51
Cavity design
In addition to the proper choice of nonlinear crystal and the pump source, efficient operation of OPOs require a perfect resonator design. Figure 2.9 shows
the typical cavity designs used for OPOs. The linear cavity, V-cavity and
X-cavity are standing-wave cavities, while the ring cavity is a travelling-wave
cavity. The pump beam is focused at the centre of the nonlinear crystal, and
the mirrors used have radius of curvature to match the mode of the resonant
wave to the pump mode. The standing-wave cavities offer the possibility of
double-pass pumping to reduce the threshold in SROs. However, an optical isolator is required in such cases to avoid any back-reflection into the laser
pump source. On the other hand, ring cavity has several advantages over other
configurations, particularly for cw OPOs, which are more sensitive to losses.
In the ring cavity, the single-pass of the resonating wave through the crystal
for every round-trip reduces the losses due to material absorption and crystal
coatings, which results in reduction of the threshold pump power. Additionally, it offers the possibility of introducing etalons for frequency selection, or
suitable nonlinear crystals for intracavity frequency conversion, at the second
beam waist of the cavity. For attaining optimum performance of an OPO, the
confocal parameter of the pump beam, bp , which is twice the Rayleigh range
needs to be equal to that of the resonating beam, bs (bp ∼bs ). To achieve this,
the focal point of the pump needs to be at the same position (at the center of
the nonlinear crystal) as the focal point of the resonating beam. To design the
above mentioned configurations, we used ABCD matrix, and calculated the
effect of optical elements on the parameters of a Gaussian beam [55,56]. Using
the Gaussian beam transformation matrices, the signal waist can be calculated
at any position in the cavity.
The beam waist, w(z), and the radius of curvature, R(z), of a Gaussian
52
2.9. Cavity design
Figure 2.9: Various OPO cavity designs: (a) Linear cavity, (b) V-cavity, (c) X-cavity, (d)
Ring cavity.
beam propagating in a straight line along z-axis are given by,
w(z) =
and
w02
z2
1+ 2
z0
z2
R(z) = z 1 + 02
z
!
(2.44)
!
(2.45)
where w 0 is the minimum beam waist at z=0, and z 0 =πnw02 /λ is known as
Rayleigh range, n is the refractive index, and λ is the wavelength of the Gaussian beam. The confocal parameter is given by b=2z 0 . Gaussian beam at a
distance z can be expressed using a complex beam parameter, given as
q(z) = z − iz0
(2.46)
The complex parameter, q(z), contains information on w(z) and R(z) both,
and is expressed as
1
1
λ
=
−i
q(z)
R(z)
πnw2 (z)
(2.47)
The ABCD matrices, also know as ray matrices, relate the complex beam
Chapter 2. Basics of nonlinear optics
53
Propagation over a distance, d
Refraction at a flat surface separating two media of index, n 1 and n 2
Thin lens of focal length, f

1 d


0

1

1
0

0
n1
n2



1
0


− f1
0

Table 2.2: Ray matrices
parameter, q2 , at a plane 2 to the value, q1 , at plane 1 as
q2 =
Aq1 + B
Cq1 + D
(2.48)
The general form of the ABCD matrix is given by

 A
M =

B 

C D
(2.49)
where A, B, C , D are the ray matrix elements. The ray matrix analysis is a
convenient way to describe the ray propagation through different media, such
as lenses, nonlinear crystals and mirrors, as a sequence of events that can be
combined by matrix multiplication to yield a final result. Some useful ray
matrices are shown in the Table 2.2.
Using these ray matrices and satisfying the condition for stability of the
cavity, -1≤(A + D)/2≤1, we can calculate the beam waist radius, starting
from center of the nonlinear crystal, and design a stable cavity. The typical
cavity design plot for ring configuration is shown in Fig. 2.10, from which the
various design parameters such as the distance between the cavity mirrors and
optimum position of the crystal can be estimated.
2.10
Active mode-locking
When the oscillating modes inside an optical oscillator, comprising a suitable
gain medium, are forced to maintain equal frequency spacing with a fixed phase
54
2.10. Active mode-locking
Figure 2.10: Signal beam waist along the ring cavity.
relationship to each other, the optical oscillator is said to be mode-locked.
For generating short optical pulses, the mode-locking of laser oscillators are
commonly used [57, 58]. However, as described in section 2.7.4, OPOs are
the potential candidate to increase the wavelength tunability. For OPOs, it
has been shown earlier [59] that synchronous pumping is the only option for
generating ultrashort pulses, because a parametric device is not able to store
the pump energy for use at later times. However, with the advent of QPM
materials, it is now possible to actively mode-lock OPOs. It has been shown
that there is a strong analogy between laser and OPO mode-locking, when
the pump depletion is negligible [60]. The basic idea is to employ amplitude
modulation or phase modulation. Here, we consider frequency modulation, as
the work presented in this thesis is based on this method.
Treating the mode-locking process in the time domain, the optical pulse in
Chapter 2. Basics of nonlinear optics
55
the Gaussian form is given by [61]
2
2
E(t) = E0 e−At e[j (ωt+Bt )]
(2.50)
where A determines the Gaussian envelope of the pulse and jBt is a linear
frequency shift during the pulse chirp. The product of pulse duration, ∆τ ,
and bandwidth, ∆f , for the Gaussian pulse is given by
2ln2
π
∆τ ∆f =
!s
B
1+
A
2
(2.51)
For |B| = A, ∆τ ∆f = 0.626. The pulse width is proportional to two parameters of the phase modulator, the modulation index, µm , and the modulation
frequency, νm . This can be expressed as [62]
∆τ ∝
1
µm
!1 4
1
νm
1
2
(2.52)
The phase modulator drive power, P m , varies the modulation index as,
µm =
q
Pm
(2.53)
−1
(2.54)
Hence, from equation 2.52,
∆τ ∝ Pm 8
Equations 2.52 and 2.54 show that the pulses shorten very slowly with
increased modulation drive, while the fastest way of pulse shortening is to
increase the modulation frequency. The dependence of peak optical power,
P pk , on average optical power, P avg , and on µm and νm is given by [62]
1
Ppk ∝
4
Pavg µm
1
2
(2.55)
νm
In the frequency domain, the modulation index is given by [63]
µm =
ζ∆Ω
π∆ν
(2.56)
56
2.10. Active mode-locking
where ∆Ω=c/2L is the frequency separation between two modes, c is the
speed of light in vacuum, L is the length of the cavity, ζ is single-pass phase
retardation, and ∆ν is the modulation frequency detuning, given by ∆ν =
νm − ∆Ω.
Chapter 3
High-power, cw, fiber-based
source at 970 nm
This chapter constitutes the following publication:
1. 13.1 W, high-beam-quality, narrow-linewidth continuous-wave fiber-based
source at 970 nm
K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh
Opt. Express 19, 11631-11637 (2011)
3.1
Motivation
High-power, continuous-wave (cw) laser sources at 970 nm are of considerable interest for a variety of scientific and technological applications including
pumping of solid-state and fiber lasers, spectroscopic detection of ozone, watervapor, and CO2 in the atmosphere, and various medical applications [64–67].
In particular, a narrow-linewidth source at 970 nm offers potential impact for
bio-sensing applications [67]. Such sources could also be deployed in combination with nonlinear frequency up-conversion schemes such as second-harmonic-
58
3.1. Motivation
generation (SHG) to provide high-power cw blue radiation to replace bulky
water-cooled argon-ion lasers, which inherently operate in multiple longitudinal modes [68]. For many such applications, a high spatial beam quality in
addition to high output power is imperative. To date, the possible sources
of 970 nm radiation are high-power diode lasers, but their beam quality still
remains an important limitation [69, 70]. The Ti:sapphire laser can provide
output radiation at 970 nm, but the low gain far from the emission peak results in low output power [71]. Optically-pumped semiconductor lasers are
another alternative source of 970 nm radiation, but limited progress has been
achieved in this direction so far [72]. High-power, cw, ytterbium (Yb)-doped
photonic crystal fiber lasers have been recently demonstrated near 980 nm,
but it has been shown that the beam quality factor degrades with the increase
in output power [73]. Although these sources provide high conversion efficiencies and have proved highly effective [70, 72, 73], the attainment of good beam
quality with good M 2 factor and narrow linewidth together with high-power
at 970 nm, and in a simple design, still remains a challenge. It is, thus, desirable to explore alternative techniques for the generation of cw radiation at
970 nm in a simple, compact and cost-effective design to provide a practical
high-power source with good spatial beam quality, mandatory requirements
for many applications.
Advances in cw fiber lasers together with the development of quasi-phasematched (QPM) ferroelectric materials provide a unique opportunity for the
realization of high-power cw sources in new spectral regions using nonlinear
frequency conversion techniques. In a particularly simple, compact and practical scheme, we recently reported direct single-pass (SP) SHG of cw Yb-fiber
lasers in MgO-doped periodically-poled stoichiometric LiTaO3 (MgO:sPPLT),
providing 13 W of green radiation at an unprecedented conversion efficiency as
high as 56% [44, 74]. With progress in cw thulium (Tm)-fiber laser technology
near 2 µm, such techniques can now be effectively exploited for the generation
Chapter 3. High-power, cw, fiber-based source at 970 nm
59
of high-power cw radiation near 1 µm at high efficiency and in good beam quality. In the pulsed regime, Frith et al. [75] demonstrated frequency-doubling of
gain-switched Tm-doped fiber laser at 1908 nm in periodically-poled LiNbO3
(PPLN), generating ∼1 W of average power at 954 nm with 60% conversion
efficiency.
In this chapter, we demonstrate the generation of multiwatt cw radiation at
970 nm by exploiting SP-SHG of a high-power cw Tm-fiber laser in combination with PPLN as the doubling crystal. Using a 40-mm crystal, we generate
an output power of 13.1 W at 970 nm with a SP-SHG conversion efficiency
of 32.7%. The output at 970 nm is in a TEM00 spatial mode with M 2 <1.6
and exhibits narrow linewidth with passive power stability better than 1.4%
(1σ value) over 1 hour. To the best of our knowledge, this is the first demonstration of SHG of cw Tm-fiber laser, which provides a compact, practical,
and efficient source of high-power radiation at 970 nm in high beam quality
and simplified design, and with competitive performance over alternative cw
sources in this wavelength range.
3.2
Experimental setup
The schematic of the experimental setup is shown in Fig. 3.1. The fundamental
source is a cw Tm-fiber laser (IPG Photonics, TLR-50-1940-LP), delivering up
to 44 W of output power at 1940 nm in a linearly-polarized beam with a quality
factor of M 2 =1.2 and a measured linewidth of ∆λ∼0.5 nm. A Faraday isolator
with an isolation of ∼23 dB is used at the output end of the fiber to prevent
back-reflection into the laser. The frequency stability of the fiber laser at the
maximum power is recorded to be better than 3.3 GHz over 2 hours. The
nonlinear crystal is 40-mm-long, 11.5-mm-wide, 1-mm-thick, undoped PPLN
sample with multiple gratings, ranging in period from Λ=25.5 to Λ=28.7 µm.
The calculated spectral acceptance bandwidth of the PPLN crystal for SHG at
60
3.3. Results and discussion
1940 nm is 3.52 nm.cm, resulting in 0.88 nm for the 40 mm interaction length
used in this experiment [52]. This value is larger than the Tm-fiber laser
fundamental linewidth, ensuring efficient SHG to 970 nm. The reflectivity of
the crystal input face at 1940 nm is experimentally measured to be R<6%,
resulting in a small input loss at the fundamental. The crystal is housed in an
oven with a stability of ±0.1 o C, which can be tuned from room temperature
to 200 o C. The fundamental beam is focused at the center of the crystal using a
CaF2 focusing lens. Although a fundamental power of up to 44 W is available
at the output of the fiber laser, due to non-optimized optics used to deliver
the pump beam, the maximum power at the input of the crystal is 40 W. We
used the Λ=28.2 µm grating period only, as it is quasi-phase-matched for SHG
at 970 nm at a temperature of 93.8 o C. A dichroic mirror (R>99.8% @ 1940
nm and T >86% @ 970 nm), is used to separate the unconverted fundamental
from the second-harmonic output beam.
Figure 3.1: Schematic of the experimental setup.
3.3
3.3.1
Results and discussion
Optimization of the SHG operation
For the attainment of the highest SHG efficiency, we studied different spatial
mode-matching conditions. Using lenses of different focal lengths, we focused
the fundamental beam to waist radii of w o ∼55.5, 45, 37.5, and 30.5 µm at
the center of the crystal, corresponding to confocal focusing parameters of
Chapter 3. High-power, cw, fiber-based source at 970 nm
61
ξ=l/b=1.88, 2.86, 4.12 and 6.23, respectively [76]. Here, l is the length of
the crystal and b is the confocal parameter, which is twice the Rayleigh range.
Figure 3.2 shows the maximum SHG efficiency achieved, at the maximum input
fundamental power of 40 W, as a function of ξ. As evident, the SHG efficiency
increases with the confocal focusing parameter, reaching as high as 32.7% at
ξ∼2.86. Further increase in ξ value results in the drop in SHG efficiency. It is
interesting to note that at ξ∼2.86, the maximum efficiency is achieved, which
is almost equal to optimum focusing parameter, ξ∼2.84, predicted by Boyd
and Kleinman in the cw limit [76].
Figure 3.2: SHG efficiency at maximum fundamental power, as a function of focusing parameter, ξ=l/b.
3.3.2
Variation in phase-matching temperature with beam waist
At maximum fundamental power of 40 W, we recorded the phase-matching
temperature, T QP M , as a function of ξ, as shown in Fig. 3.3(a). As evident, the
phase-matching temperature decreases with increase in ξ and has a steep fall
towards tighter focusing. This may be attributed to the thermal effects arising
from the tighter focusing of pump beam in the crystal, resulting in increase of
62
3.3. Results and discussion
thermal load, hence requiring a decrease in the required external heat applied
to the crystal to achieve phase-matching. Another possible reason could be the
increase in angular divergence of the beam with tighter focusing, which results
in the propagation of the divergent components of the fundamental beam over
longer grating periods, resulting in a shift in the peak phase-matching temperature. We calculated the propagation length of the divergent components, and
the corresponding change in phase-matching temperature, for a propagation
distance corresponding to grating period of Λ=28.2 µm along the crystal, as
a function of beam waist radius. The results are shown in Fig. 3.3(b). It
is found that under loose focusing (w o ∼55.5 µm), the most divergent components of the fundamental beam propagate over an increased grating period of
28.20175 µm, while for tight focusing (w o ∼30.5 µm) the increased grating period for the most divergent components is 28.20575 µm. Therefore, in reducing
the beam waist from w o ∼55.5 µm to w o ∼30.5 µm, the grating period for the
most divergent components increases by 4 nm, resulting in an average decrease
in phase-matching temperature of the crystal with increased divergence and
tighter focusing, as observed in Fig. 3.3(a). Using a wavemeter (Bristol, 721BIR, absolute accuracy of 1 ppm), we measured the central wavelength (λω ) of
the fundamental beam at 40 W to be λω =1941.5 nm. Figure 3.3(c) shows the
variation of theoretical predicted values of phase-matching temperature with
focusing parameter, ξ, calculated for a single-frequency fundamental, using
relevant Sellmeiers equation [77]. The theoretical T QP M curve shows the same
behavior as that of the experimental curve of Fig. 3.3(a).
To avoid any thermal contribution, we further measured the phase-matching
temperatures for different beam waists, at low fundamental power. The results
are shown in Fig. 3.3(d), where it is observed that at an input power of
∼1 W, where thermal effects are negligible, the phase-matching temperature
increases with loose focusing, as also seen for high fundamental power (Fig.
3.3(a)). With negligible contribution from thermal effects, the change in T QP M
Chapter 3. High-power, cw, fiber-based source at 970 nm
63
is attributed mainly to the fundamental beam divergence in the crystal.
Figure 3.3: (a) Phase-matching temperature at maximum fundamental power, as a function
of focusing parameter, ξ. (b) Theoretically calculated propagation length for divergent
components and the corresponding change in phase-matching temperature, as a function of
beam waist radius. (c) Theoretically calculated phase-matching temperature, as a function of
focusing parameter, ξ. (d) Phase-matching temperature under different focusing conditions,
at pump power of ∼1W.
3.3.3
Variation in phase-matching temperature with pumping level
Figure 3.4(a) shows the phase-matching temperature as a function of fundamental power for w o ∼45 µm (ξ∼2.86), where we observe a rise in phasematching temperature with the increase in fundamental power. We obtain
T QP M ∼112 o C at 0.8 W and 119.5 o C at 40 W, corresponding to a difference
in phase-matching temperature of 7.5 o C. We measured the central wavelength
of the fundamental output at different power levels using the wavemeter and
64
3.3. Results and discussion
found that the peak wavelength shifts towards the longer value with the rise
in fundamental power. For example, λω =1939.8 nm at ∼1 W, and 1941.5 nm
at ∼40 W of fundamental power, which corresponds to a change of 1.7 nm in
central wavelength. We theoretically calculated the phase-matching temperature as a function of fundamental wavelength considering negligible thermal
effects [77]. As seen in Fig. 3.4(b), an increase in the fundamental wavelength
by 1.7 nm corresponds to an increase of 7.4 o C in phase-matching temperature,
thus confirming the observed rise in the phase-matching temperature with the
increase in fundamental power.
3.3.4
Temperature acceptance bandwidth
To characterize the crystal under different focusing conditions, we measured
the temperature acceptance bandwidths for different beam waists. The measurements were performed at low fundamental power, in order to avoid any
thermal contributions. Figure 3.5(a) shows the result for optimum focusing
(w o ∼45 µm), together with the sinc 2 fit, at a fundamental power of ∼1 W. The
measured full-width-half-maximum (FWHM) temperature acceptance bandwidth (∆T ) is found to be 5.9 o C at T QP M =113 o C. This is larger than the
theoretical value of ∆T =3.8 o C at T QP M =93.8 o C for the 40-mm crystal,
which has been calculated for a single-frequency fundamental in plane-wave
approximation without focusing, using the relevant Sellmeier equations [77].
The discrepancy between the experimental and theoretical value of ∆T could
be in part due to the finite bandwidth of the fundamental (∆λ∼0.5 nm), while
the discrepancy in the value of T QP M could be due to possible non-uniformity
in the grating period along the crystal length. The difference between the
experimental and theoretical values of ∆T could also in a large part be attributed to the focusing of the fundamental beam. As noted in section 3.3.2,
this can give rise to an average increase in the grating period for all spatial
components, which results in a decrease in the peak phase-matching tempera-
Chapter 3. High-power, cw, fiber-based source at 970 nm
65
Figure 3.4: (a) Phase-matching temperature versus fundamental power. (b) Theoretically
calculated change in phase-matching temperature versus fundamental wavelength for the
grating period of Λ=28.2 µm.
66
3.3. Results and discussion
ture, T QP M , as well as a broadening of the phase-matching bandwidth towards
lower temperatures, resulting in an increase in the experimental value of ∆T .
At the input power of ∼1 W, we measured the variation of the FWHM
temperature acceptance bandwidth as a function of fundamental beam waist
radius. It is clear from Fig. 3.5(b) that for tighter pump focusing, the temperature acceptance bandwidth increases, as predicted. On the other hand,
we also theoretically calculated the temperature acceptance bandwidth of the
40-mm-long PPLN crystal as a function of phase-matching temperature, in the
plane-wave limit in the absence of focusing, and confirmed an increase in ∆T
with the decrease in phase-matching temperature [52]. Therefore, the inherent
variation of ∆T and T QP M in the plane-wave limit combined with the focusing
effects lead to the observed behavior in Fig. 3.3(d) and Fig. 3.5(b).
3.3.5
SHG power scaling and stability
The variation of SHG power and the corresponding efficiency up to the maximum available fundamental power for ξ∼2.86 is shown in Fig. 3.6. We obtained 13.1 W of SHG power at 970 nm for 40 W of input power to the crystal,
representing a single-pass efficiency of 32.7%. As seen in Fig. 3.6, the SHG
power has a quadratic dependence on the fundamental power up to 18.5 W,
beyond which it increases linearly, implying saturation of SHG efficiency at
higher power. This can be attributed to pump depletion, back-conversion and
thermal de-phasing effects in the PPLN crystal. However, we confirmed the
role of thermal effects to be negligible, by performing power scaling measurements with tight focusing at w o ∼37.5 µm (ξ=4.12) under quasi-cw condition.
This measurement was performed by chopping the beam at 530 Hz with a duty
cycle of 5%, and then comparing the results with that under cw condition. In
both the cases, we found the SHG efficiency saturation at higher power, with
a maximum efficiency of ∼26%. Using the slope of the generated SHG power
Chapter 3. High-power, cw, fiber-based source at 970 nm
67
Figure 3.5: (a) Temperature phase-matching curve for SHG at w o ∼45 µm, and (b) temperature acceptance bandwidth under different focusing conditions. Pump power is ∼1 W.
68
3.3. Results and discussion
versus square of the fundamental power curve, we also calculated the effective
nonlinear coefficient for our PPLN crystal at 1940 nm wavelength [50], which
we found to be d ef f ∼13.6 pm/V. Similar d ef f values were obtained from measurements at different beam waists and under quasi-cw condition.
We measured the power stability near the maximum SHG power at the
fundamental power of 40 W. The result is shown in Fig. 3.7(a), where we obtained a passive stability better than 1.4% (1σ value) over 1 hour, without any
precautions. The SHG power fluctuation is mainly attributed to the changes
in the laboratory environment and also to some extent to the fluctuations in
the input pump power with 0.9% (1σ value) over 1 hour, as seen in Fig. 3.7(b).
Improved thermal and mechanical isolation of the system with proper temperature control and increased pump power stability can further enhance the SHG
power stability.
Figure 3.6: SHG power and the corresponding conversion efficiency as a function of incident
fundamental power at w o ∼45 µm.
3.3.6
SHG single-frequency operation and beam quality
We also recorded the spectrum of the generated SHG output at maximum
power and found the linewidth (∆λ2ω ) below 0.3 nm, as shown in Fig. 3.8,
Chapter 3. High-power, cw, fiber-based source at 970 nm
69
Figure 3.7: Time trace at maximum power of (a) generated SHG output, and (b) input
fundamental over 1 hour.
limited by the resolution of our spectrum analyzer. The generated secondharmonic linewidth is thus narrower than that of the fundamental, as expected.
The far-field energy distribution of the SHG beam at maximum power together with the intensity profile is shown in Fig. 3.9. The slight asymmetry
seen in the beam profile is due to the small tilt angle of the lens and separation mirror from the normal incidence. Using a f =100 mm focal length lens
and a scanning beam profiler, the beam quality factor of the SHG beam at
maximum power was measured to be M x 2 ∼1.43 and M y 2 ∼1.6, confirming the
TEM00 spatial mode.
We did not observe any photorefractive damage in the PPLN crystal up
to the maximum SHG power, as evident from the output power stability and
beam quality.
3.4
Conclusions
In conclusion, we have demonstrated, for the first time, efficient SP-SHG of
a cw Tm-fiber laser, providing multiwatt cw radiation at 970 nm at high
70
3.4. Conclusions
Figure 3.8: Spectrum of SHG output at maximum power.
Figure 3.9: Far-field TEM00 energy distribution of the generated SHG beam. The thin
curves are the intensity profiles along the two orthogonal axes.
Chapter 3. High-power, cw, fiber-based source at 970 nm
71
efficiency, in narrow linewidth and high beam quality, and with good stability.
By deploying a 40-mm-long PPLN crystal, we have generated 13.1 W of cw
output power at 970 nm at single-pass conversion efficiency as high as 32.7%.
The SHG output has a linewidth below 0.3 nm with a power stability better
than 1.4% (1σ value) over 1 hour, and has a TEM00 beam profile with M 2 <1.6.
The absence of thermal effects suggest the possibility of further increase in cw
SP-SHG output power and efficiency by using longer crystals, higher pump
powers, and narrower fundamental linewidths. The exploitation of multicrystal
scheme using several PPLN crystals in a cascade [44] could also lead to further
increases in SP-SHG efficiency to >50%, providing >20 W of cw output power
at 970 nm. The demonstrated fiber-based device offers a viable, compact
and practical source of high-power, linearly-polarized, narrow-linewidth, and
high-beam-quality cw radiation at 970 nm, with competitive performance over
alternative sources in this wavelength range, and offering promise for a variety
of applications.
Chapter 4
Interferometrically
output-coupled cw SRO
This chapter constitutes the following publication:
1. Antiresonant ring output-coupled continuous-wave optical parametric os-
cillator
K. Devi, S. Chaitanya Kumar, A. Esteban-Martin,
and M. Ebrahim-Zadeh
Opt. Express 20, 19313-19321 (2012)
4.1
Motivation
Continuous-wave (cw) optical parametric oscillators (OPOs) in singly-resonant
oscillator (SRO) configuration are now firmly established as viable sources
of tunable high-power coherent radiation [5], nearly two decades after their
first demonstration [30]. Due to the substantially lower intensities available
from cw pump lasers, resulting in lower nonlinear gain and high oscillation
threshold, the development of cw OPOs in SRO design remained particu-
74
4.1. Motivation
larly challenging for many years. However, with the advent of quasi-phasematched (QPM) nonlinear materials, together with advances in high-power
pump sources, particularly fiber lasers, cw SROs with wide tuning range and
high output power have been realized, covering spectral regions from the visible to mid-infrared [41, 46, 78–82]. The high optical nonlinearity together with
long interaction lengths and noncritical phase-matching in QPM materials has
enabled operation of cw SROs at practical pump power thresholds (watt-level)
and elevated output power levels (>10 W) [41, 81]. Operation of cw SROs
based on QPM materials is now sufficiently robust that for the attainment of
highest extracted power, limited output coupling of the resonant signal wave
can be tolerated [83]. This enables substantial enhancement not only in the
total (signal plus idler) output power and external efficiency, but also in the
usable tuning range. At the same time, the use for signal output coupling has
been shown to be imperative at increased pump powers, where the high intracavity signal intensities can lead to significant thermal loading in the nonlinear
crystal, limiting conversion efficiency and degrading output power, wavelength
stability and beam quality [39, 84, 85]. As such, the deployment of signal
output coupling represents an important strategy to achieve optimum performance in cw SROs with regard to several important operating parameters. As
in laser oscillators, the conventional technique for the attainment of output
coupling in cw SROs relies on the use of different output coupler (OC) mirrors
with discrete transmission values at the resonant wavelength [41]. However,
this approach requires the search for different OC mirrors to obtain the optimum value of output coupling. Moreover, under different cw SRO operating
conditions, such as the resonant wavelength and pumping level, the optimum
value of output coupling can change, making absolute optimization of output
power at all wavelengths and under all operating conditions difficult, costly,
and time-consuming.
Recently, an alternative new approach for absolute optimization of ex-
Chapter 4. Interferometrically output-coupled cw SRO
75
tracted power from optical oscillators was demonstrated using an antiresonant
ring (ARR) interferometer as an output coupler, and the concept was realized for the first time in a femtosecond OPO [86]. Later, the technique was
extended to traveling-wave oscillators, where optimum output coupling in a
picosecond OPO configured in a ring resonator was demonstrated [87]. The
ARR interferometer essentially consists of two highly reflecting mirrors (M),
and a beam-splitter (BS) with a transmittance, T, and reflectance, R, as shown
in Fig. 4.1. The BS splits the incident optical beam (E in ) into clockwise (dotted) and anticlockwise (solid) beams. These counter-propagating beams, after
propagation inside the ring, are then again transmitted and reflected at the BS.
The new pairs of fields, (E r ccw ;E t cw ) and (E t ccw ;E r cw ), thus formed, interfere,
and give rise to reflected, E r =E r ccw +E t cw , and transmitted, E t =E t ccw +E r cw ,
output fields. The power reflected back is given by RARR =4RT , while the
power transmitted out of the ARR is given by TARR = |R − T |2 , implying that
the reflected fields from the ARR and the transmitted fields through the ARR
interfere constructively and destructively, respectively. The ARR output coupling technique exploits the ability to adjust the T :R ratio of the BS simply
by varying the angle of incidence (θBS ) on the BS. This results in a change
in the transmitted power, T ARR , from the ARR, which can then be used as a
means to vary the optical feedback into an optical oscillator incorporating the
ARR.
In this chapter, we demonstrate, for the first time, the integration of an
ARR interferometer into a cw SRO, for the attainment of optimum output
coupling. While the technique has been previously demonstrated in pulsed
optical oscillators [86, 87], where high levels of output coupling (>50%) can
be readily supported, the integration of such an ARR into a cw SRO can be
challenging due to the low tolerance of cw SROs to loss and output coupling
(typically <5%). We demonstrate that despite the high sensitivity to loss and
output coupling, the ARR offers a unique and practical approach to achieve
76
4.2. ARR output-coupled cw SRO
Figure 4.1: Antiresonant ring interferometer.
fine, adjustable, and in situ optimization of output power from cw SROs.
4.2
4.2.1
ARR output-coupled cw SRO
Experimental setup
The schematic of the experimental setup is shown in Fig. 4.2. The fundamental pump source is a cw Yb-fiber laser (IPG Photonics, YLR-30-1064-LPSF), delivering up to 30 W of output power at 1064 nm in a single-frequency,
linearly-polarized beam with a spatial quality factor of M 2 ∼1.01 and a nominal linewidth of 89 kHz. A Faraday isolator (FI) with an isolation of ∼25
dB was used at the output end of the fiber to prevent back-reflection into the
laser. To maintain stable output characteristics, we operated the pump laser
at maximum output power and attenuated the power using a combination of a
half-wave plate (HWP) and a polarizing beam-splitter (PBS). A second HWP
was used to control the pump polarization for phase-matching in the nonlinear crystal, which is a 50-mm-long, 6.2-mm-wide, 1-mm-thick, 5% MgO-doped
Chapter 4. Interferometrically output-coupled cw SRO
77
periodically-poled LiNbO3 (MgO:PPLN). The crystal was housed in an oven
with a stability of ±0.1 o C and adjustable from room temperature to 200 o C.
The crystal contains five gratings with periods ranging from Λ=29.5 µm to
Λ=31.5 µm, in steps of 0.5 µm. However, we only used the Λ=31.5 µm grating period in this work, providing a theoretical wavelength tuning range of
1663-1944 nm for the signal and 2954-2350 nm for the idler, for the crystal
temperature varying from 25 o C to 200 o C. A lens of focal length, f =250 mm,
was used to focus the fundamental beam at the centre of the crystal. The OPO
Figure 4.2: Schematic of the experimental setup. FI: Faraday isolator, λ/2: Half-wave
plate, PBS: Polarizing beam-splitter, L: Lens, M1−5 : Mirrors, M: Dichroic mirror, BS:
Beam-splitter.
was configured in a standing-wave cavity, comprising two concave mirrors, M1
and M2 (r=150 mm), one plane mirror (M3 ) in one arm, and an ARR interferometer formed by two plane mirrors (M4 and M5 ) and a BS integrated into the
other arm. For the BS, we used a standard, low-cost, commercial fused silica
plate available in our laboratory. The plate was 3-mm-thick with broadband
coating over 0.9-2.6 µm. Such a BS could allow output coupling optimization over a broad spectral range, given the simplicity and effectiveness of the
ARR technique. However, in this work we only performed the measurements
at a fixed signal wavelength, using a single grating period to demonstrate the
concept in a cw SRO, for the first time. All the OPO mirrors (M1−5 ) were
78
4.2. ARR output-coupled cw SRO
highly reflective (R>99%) for the signal (1.3-1.9 µm) and highly transmitting
(T >90%) for the idler (2.2-4 µm), ensuring SRO operation. The mirrors are
also highly transmitting (T >92%) for the pump. A dichroic mirror, M, was
used to separate the pump from the generated idler beam. The total SRO cavity length was LSRO =183 cm, which was the sum of the standing-wave cavity
length (2Llinear =166.8 cm) and length of the ARR interferometer (Lring =16.2
cm).
4.2.2
Design and optimization of the cavity
In order to optimize the SRO, we used a focusing parameter [76],
ξ=
l
bp
(4.1)
where bp is the confocal parameter of the pump, defined as
k
wp
(4.2)
2πnp
λp
(4.3)
bp =
with
k=
Here, l=50 mm is the length of the nonlinear crystal, np , λp , w p are the refractive index, wavelength and waist radius of the pump beam inside the nonlinear
crystal, respectively. In this experiment, the pump beam is confocally focused
to a beam waist radius of w p =63 µm, corresponding to a focusing parameter of
ξ=l/bp ∼1, while the design of the SRO cavity resulted in a signal beam waist
radius of w s =76 µm at the centre of the nonlinear crystal. Thus, the cavity
design ensures optimum overlap of pump and resonant signal at the center of
the crystal (bp ∼bs ).
Chapter 4. Interferometrically output-coupled cw SRO
4.3
4.3.1
79
Results and discussion
Conventional 5% output-coupled SRO
Power scaling
Initially, we performed the power scaling of the cw SRO with a conventional
5% OC mirror in place of the ARR output coupler (ARR-OC). The total
SRO cavity length was 2Llinear =2×91.5 cm = 183 cm, equal to that of the
ARR output-coupled SRO (ARR-OC-SRO). In both configurations, we used
the same focusing condition for the pump and adjusted the cavity for optimum
overlap between the pump and the signal beam in the cold cavity. We operated
the SRO at the center of the tuning range for the Λ=31.5 µm grating, and
generated a signal wavelength of λsignal =1706 nm and a corresponding idler
wavelength of λidler =2826 nm, maintaining the crystal temperature at 88.5 o C.
Figure 4.3 shows the variation of signal, idler and the total power (signal plus
idler) as a function of pump power for the conventional 5% output-coupled
SRO (OC-SRO). We obtained a signal power of 4.56 W and idler power of
4.09 W at a maximum pump power of 28.6 W. The total power extracted at
the maximum pump power was thus 8.65 W.
4.3.2
Variable output coupling
In order to perform output coupling optimization using the ARR technique,
we first characterized the ARR interferometer prior to integration into the cw
SRO by evaluating the transmission of output signal wavelength through the
ARR at different angles, θBS , external to the SRO cavity. We measured the
input power into the ARR and the output power from the ARR at a fixed signal
wavelength (1706 nm), and estimated the ARR transmission as a function of
the incident angle, θBS , on the BS. The result is shown in Fig. 4.4, where it
can be seen that with the increase in θBS from 20o to 40o , the transmission
80
4.3. Results and discussion
Figure 4.3: Variation of signal and idler power along with the total power extracted from
the OPO using conventional 5% OC as a function of input pump power.
of the ARR increases continuously from 0.8 to 7.3%. Since the performance
of cw SRO depends strongly on the cavity losses, we estimated the additional
average loss due to the ARR elements. By measuring the transmitted and
reflected power from the BS at different θBS , the total average BS loss at
1706 nm was found to be ∼1.5% throughout the BS angular range, while the
extra mirror (M5 ) introduced an additional coating loss of ∼0.5%. Therefore,
with the available BS and mirror M5 , the characterization of the ARR-OCSRO, as described below, was performed in the presence of an additional loss
background of ∼2%. By using a more optimum BS and mirror combination
with lower insertion loss, we expect significant improvements in ARR-OC-SRO
performance with regard to output power and pump threshold.
After external characterization, we integrated the ARR into the cw SRO
cavity. In order to determine the optimum ARR-OC value for the signal, we
varied θBS continuously, as we did in external characterization. We performed
power scaling measurements for different angles of incidence, θBS , at a signal
wavelength of 1706 nm (idler at 2826 nm), by recording the signal output
power from the ARR-OC-SRO, and the corresponding single-pass idler power
from the oscillator.
Chapter 4. Interferometrically output-coupled cw SRO
81
Figure 4.4: Transmission from ARR interferometer as a function of BS angle, θBS .
4.3.3
Output coupling optimization at different pumping levels
Experimental
To study the behavior of simultaneously extracted signal and idler power with
the increase in the ARR transmission, and hence to obtain the absolute value
of optimum ARR-OC at different pumping levels, we optimized the cw ARROC-SRO for input powers of 15.9 W and 23.2 W. Figures 4.5(a) and 4.5(b)
show the output coupling optimization of signal at pump powers of 15.9 W and
23.2 W, respectively, by varying the BS angle, θBS . As seen in Fig. 4.5(a), the
signal power increases from 0.54 W at θBS =20o (T ARR =0.8%) to a maximum
value of 1.22 W at θBS =22o (T ARR =2%). Further increasing the BS angle
beyond θBS =22o results in the drop of signal power to 0.87 W at θBS =25o
(T ARR =2.1%), confirming 2% as the optimum ARR-OC value for the signal at
15.9 W of pump power. Measurements beyond θBS =25o were not possible due
to the increase in the threshold power. Similarly, at a pump power of 23.2 W,
seen in Fig. 4.5(b), the signal power increases from 1.15 W to a maximum value
of 2.28 W at θBS =33o (T ARR =4.6%). Further increasing the BS angle results
in the drop of signal power to 1.64 W at θBS =40o (T ARR =7.3%), confirming
82
4.3. Results and discussion
4.6% as the optimum ARR-OC value for the signal at 23.2 W of pump power.
This clearly shows the potential of the ARR technique for in situ optimization
of output power from the cw SRO (or any optical oscillator) under different
operating conditions, including different pumping levels.
Figure 4.5: Optimization of signal power versus BS angle, θBS , at input pump power of (a)
15.9 W, and (b) 23.2 W.
Figure 4.6(a) and 4.6(b) show the simultaneously extracted single-pass idler
power at pump powers of 15.9 W and 23.2 W, respectively, as a function of
BS angle. As evident from Fig. 4.6(a), at a pump power of 15.9 W, the idler
power decreases from 2.35 to 1.79 W for an increase in θBS from 20o to 25o .
Similarly, at a pump power of 23.2 W, the idler power decreases gradually from
3.36 to 3.15 W for an increase in θBS from 20o to 32o , and has a sharp fall
with further increase of θBS beyond the optimum angle of θBS =33o , up to 40o .
The decrease in the idler power with the increase in θBS can be attributed to
the increasing output coupling loss of the resonating signal wave with increase
in ARR transmission, resulting in reduced intracavity signal intensity to mix
Chapter 4. Interferometrically output-coupled cw SRO
83
with the pump to generate the single-pass idler. Thus, the idler output power
is reduced with increasing θBS (higher signal output coupling) for all pump
powers, indicating that the idler power is not necessarily maximized at the
optimum signal output coupling. Hence, the ARR also enables the possibility
of exploring the idler output power as a function of output coupling as well
as independently maximizing the signal and idler output power, which are
difficult to study with conventional discrete output couplers.
Figure 4.6: Optimization of simultaneously extracted single-pass idler power versus BS angle,
θBS , at input pump power of (c) 15.9 W, and (d) 23.2 W.
Theoretical
In order to compare the observed behavior of signal and idler power in Figs.
4.5(a) and 4.5(b), and Figs. 4.6(a) and 4.6(b) with theory, we also performed
calculations to obtain the variation of extracted signal power, and the corresponding idler power, as a function of signal output coupling. We performed
the calculations for a conventional cw OC-SRO deploying a partially transmit-
84
4.3. Results and discussion
ting mirror, while considering a fixed background cavity loss of 2%, a pump
depletion of 70%, a Gaussian pump beam profile, and assuming no thermal
effects [88–90]. The results are shown in Fig. 4.7(a) and 4.7(b) for a fixed
pump power of 15.9 W and 23.2 W, respectively. As evident, at pump power
of 15.9 W and 23.2 W, the optimum output coupling for the signal is attained
at 3.6% and 4.8%, respectively, and the corresponding idler power decreases
with increase in output coupling. The maximum idler power is obtained at
the minimum signal output coupling value for both the pumping levels, as also
observed in Fig. 4.6(a) and 4.6(b).
It is also evident from theoretical curves, Fig. 4.7(a) and 4.7(b), that with
increase in pump power, the output coupling optimization curve for signal is
broadened, which is also observed in Fig. 4.5(a) and 4.5(b). The theoretical
variation of signal and idler power as a function of output coupling in Fig. 4.7
are thus in good agreement with the experimental results shown in Fig. 4.5 and
Fig. 4.6, confirming that the ARR behaves in the same way as a conventional
output coupler.
To obtain a clearer picture, we calculated the signal output power optimization curve at a low pump power of 5 W and a high pump power of 28.6 W,
with the results shown in Fig. 4.8. As seen, at high pump power the range of
optimum output coupling values is significantly broader than at the low pump
power, where the attainment of optimum output coupling is critical.
4.3.4
Power scaling
At ARR-OC value of 33o
At the ARR-OC value of 4.6%, the power scaling of the ARR-OC-SRO is shown
in Fig. 4.9, depicting the variation of signal power, the corresponding idler
power, and the total output power as a function of input pump power. The
Chapter 4. Interferometrically output-coupled cw SRO
85
Figure 4.7: Theoretically calculated optimization curves for signal and idler power as a
function of output coupling at input pump power of (a) 15.9 W, and (b) 23.2 W.
86
4.3. Results and discussion
Figure 4.8: Theoretically calculated optimization curves for signal power as a function of
output coupling at low pump power of 5 W and high pump power of 28.6 W.
maximum signal and idler power achieved are 2.81 W and 3.88 W, respectively,
corresponding to a maximum achieved total output power (signal plus idler) of
6.69 W, representing a total extraction efficiency of 23.4%. The signal and idler
power vary linearly up to the maximum pump power of 28.6 W. The variation
of the total output power as a function of pump power also confirms the linear
dependence. It is to be noted here that although no sign of saturation in the
output power for higher pump power has been observed at the ARR-OC value
of 4.6% (θBS =33o ), we have also not observed any evidence of saturation at
lower output coupling values (smaller BS angles). This is attributed mainly to
the background loss present at all the BS angles.
The lower output power obtained from the optimal ARR-OC-SRO at 23.2
W of pump power as compared to that with the conventional non-optimal
5% OC-SRO (see Fig. 4.3) is attributed to the extra insertion loss induced
by the un-optimized BS and mirror coatings used in the present experiment,
as noted previously. Although, the maximum output power from optimal
ARR-OC-SRO has not been achieved, a background loss is present for all BS
angles, indicating θBS =33o (T ARR =4.6%) as the optimum angle for maximum
Chapter 4. Interferometrically output-coupled cw SRO
87
Figure 4.9: Signal and corresponding idler along with total output power scaling at BS
angle, θBS =33o .
output power extraction. The optimum ARR-OC value of 4.6% together in
the presence of the background insertion loss associated with the ARR results
in reduced intracavity signal power, leading to a lower maximum signal power
extraction (see Fig. 4.9) than with the 5% conventional output coupler (see
Fig. 4.3), and without any saturation in power scaling (see Fig. 4.9). By using
a BS and mirrors with improved coatings, the absolute highest signal power
can be extracted at optimum ARR-OC value. Further, with reduced insertion
loss, we can expect similar output power in the ARR-OC-SRO to that in the
conventional OC-SRO of the same output coupling.
At optimum ARR-OC values
Figure 4.10 shows the signal power extracted from the cw ARR-OC-SRO at
the optimum output coupling value versus pump power. Each data point
represents the maximum signal power at a given pump power, obtained by
measuring the extracted signal power as a function of BS angle, while keeping
the pump power fixed. As seen, the optimum signal power increases almost
linearly, reaching 2.81 W for a maximum input power of 28.6 W. The inset of
88
4.3. Results and discussion
Fig. 4.10 shows the theoretical power scaling of the signal for a conventional cw
OC-SRO, calculated at the corresponding theoretical optimum output coupling
values [88–90]. As can be seen, the theoretical power scaling shows the same
behavior as the experimental variation of Fig. 4.10.
Figure 4.10: Signal power scaling at optimum signal output coupling values. Inset: Corresponding theoretical plot.
We also measured the extracted idler power as a function of pump power
at minimum signal output coupling values corresponding to maximum idler
power, for different pumping levels, as shown in Fig. 4.11. The output coupling
for the signal, at which the idler power is maximum, always corresponds to the
lowest value (T ARR =0.8%) at θBS =20o for all pump powers. The maximum
idler power achieved is 4.2 W for a pump power of 28.6 W. The curve depicts
the linear dependence of idler power on the input pump power. The calculated
theoretical power scaling for the maximum idler [88–90] under minimum signal
output coupling is also shown in the inset of Fig. 4.11, confirming a linear
behavior similar to the experimental variation in Fig. 4.11.
4.3.5
Pump depletion, threshold pump power and beam quality
Figure 4.12 shows the corresponding pump depletion for the cw ARR-OC-
Chapter 4. Interferometrically output-coupled cw SRO
89
Figure 4.11: Idler power scaling at minimum signal output coupling values. Inset: Corresponding theoretical plot.
SRO at a fixed pump power of 23.2 W, for different BS angle. As seen, pump
depletion decreases gradually from 56.6% to 51% for an increase in θBS from 20o
to 32o , and has a sharp fall with further increase of θBS beyond the optimum
angle (θBS =33o ) of signal power extraction. It has been observed that the
pump depletion follows a similar behavior to the variation of idler power as a
function of BS angle, and thus signal output coupling, as seen in Fig. 4.6(b).
Figure 4.12: Pump depletion as a function of BS angle, θBS , at input pump power of 23.2
W.
90
4.4. Conclusions
We also recorded the cw ARR-OC-SRO threshold pump power for different
values of ARR-OC, with the results shown in Fig. 4.13. By increasing the
output coupling from 0.8% to 7.3%, the threshold pump power for the ARROC-SRO rises from 12.3 to 22.1 W, with the corresponding intracavity power
estimated to decrease from 187 to 28 W at the maximum pump power of 28.6
W. The loss due to the ARR is also evident from the comparison of threshold
power for the cw 5% OC-SRO and that for the 4.6% ARR-OC-SRO, which are
measured to be 15.1 W and 18.3 W, respectively. With reduced insertion loss,
we can expect similar pump power threshold for the ARR-OC-SRO to that in
the conventional OC-SRO of the same output coupling.
We also recorded the far-field energy distribution of the output signal from
the cw ARR-OC-SRO with θBS =33o at 23.2 W of pump power, as shown in
inset of Fig. 4.13. Using a f =100 mm focal length lens and a scanning beam
profiler, the quality factor of the signal beam was measured to be M x 2 ∼1.9
and M y 2 ∼1.9, confirming TEM00 spatial mode. We have not observed any
degradation in output beam quality due to the integration of the ARR into
the cw SRO. We do not expect any change in the beam quality with other
ARR-OC values, as we have not observed any thermal effects at lowest as well
as highest output coupling values.
4.4
Conclusions
In conclusion, we have demonstrated, for the first time to our knowledge, a versatile technique based on the use of an ARR interferometer for continuous fine
adjustment of output coupling and in situ optimization of the output power
in cw SROs. With fine adjustment of the ARR transmission, optimum output
coupling value for signal and idler can be attained at different input pumping
levels. The experimental results have also been shown to be in good agreement
with the theoretical modeling. By deploying a custom-made BS and a mirror
Chapter 4. Interferometrically output-coupled cw SRO
91
Figure 4.13: The cw SRO threshold power, P th , as a function of signal output coupling with
the ARR. Inset: far-field energy distribution of extracted signal with optimum ARR-OC
value of 4.6% at 23.2 W of input pump power.
with improved coatings, resulting in lower insertion loss, the same maximum
signal output power is expected from the cw ARR-OC-SRO as with a conventional cw OC-SRO of the same optimum output coupling. The technique is
wavelength-independent, and so can be used over an extended spectral range
with a single ARR setup. With advances in QPM materials, together with the
available broadband-coated beam-splitters, the present set up can be further
deployed over a wide wavelength range using fanned or multiple grating structures in combination with temperature tuning, indicating the potential use of
this technique for widely tunable OPOs. This proof-of-principle demonstration also opens up new possibilities for other applications of the technique in
cw optical oscillators in general, for example in the implementation of coupled
cavities or cavity dumping and mode-locking, as first suggested in the context
of lasers nearly four decades ago [91–94].
Chapter 5
All-periodically-poled, tunable,
cw, near-infrared source
This chapter constitutes the following publication:
1. High-power, continuous-wave, single-frequency, all-periodically-poled, near-
infrared source
K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh
Opt. Letters 37, 5049-5051 (2012)
5.1
Motivation
Tunable, continuous-wave (cw), single-frequency sources covering the 700–1000
nm spectral region are of considerable interest for diverse range of applications
from spectroscopy and biomedicine to pumping of optical parametric oscillators (OPOs) [34,95]. The Ti:sapphire laser, the workhorse of the near-infrared
region, is the primary source in this spectral range, catering for the majority
of applications. However, the need for bulk solid-state pump lasers and watercooling increases complexity, cost, and size of the Ti:sapphire laser. It would
94
5.1. Motivation
be desirable to consider alternative new strategies for the generation of tunable
near-infrared radiation while overcoming such limitations. Deploying compact,
robust, and efficient fiber-laser-based pump sources in the green is a practical
alternative to partly reduce the complexity of the Ti:sapphire laser [96, 97],
but direct nonlinear frequency conversion using second-harmonic-generation
(SHG) or techniques based on OPOs are other attractive alternatives to access
the Ti:sapphire wavelength range. Earlier reports on cw nonlinear frequency
conversion into the Ti:sapphire wavelength range include the generation of
high-power cw radiation at 970 nm based on single-pass SHG of a Tm-fiber
laser in periodically-poled LiNbO3 (PPLN) [98], tunable signal radiation from
an output-coupled singly-resonant OPO (SRO) based on MgO-doped stoichiometric periodically-poled LiTaO3 (MgO:sPPLT) pumped in the green [83], and
frequency-doubling of the idler output from a cw green-pumped OPO using
external enhancement [99]. Further, a narrowly tunable 629 nm source based
on a cw OPO using sum-frequency-mixing in a dual-grating PPLN crystal was
also demonstrated [100]. However, achieving tunability in combination with
high output power has remained challenging. Another attractive approach to
generate tunable radiation in 700–1000 nm spectral range is the intracavity
SHG of the resonant signal wave in SROs pumped by high-power laser sources
near 1 µm. This approach has been demonstrated in a Yb-laser-pumped picosecond OPO [101]. In cw SROs based on quasi-phase-matched (QPM) nonlinear materials such as multigrating MgO-doped periodically-poled LiNbO3
(MgO:PPLN) [41], offering wide signal tuning range and high circulating powers, internal SHG can be similarly exploited to achieve wavelength extension
into the near-infrared at high efficiency and over a broad spectral range. Moreover, with the advances in QPM materials and mature fabrication technology, it is now possible to readily access crystals such as MgO:PPLN and
MgO:sPPLT with different grating designs. In particular, MgO:sPPLT, offering high resistance to photorefractive damage below 1 µm, relatively high
Chapter 5. All-periodically-poled, tunable, cw, near-infrared source
95
nonlinearity (d ef f ∼9 pm/V), and interaction lengths up to 30 mm, are now
commercially available in fanout-grating design, providing additional advantage of continuous tuning at a fixed temperature [37]. Thus, the combination
of newly available QPM material designs, together with latest generation of
fiber lasers, can lead to the realization of efficient, compact, and tunable cw
sources for the 700–1000 nm spectral range, as a potential future alternative
to the Ti:sapphire laser for a variety of applications.
In this chapter, we demonstrate this potential by describing a high-power,
single-frequency, all-periodically-poled, near-infrared source tunable across 775–
807 nm, based on intracavity SHG of a cw SRO and pumped by a Yb-fiber
laser at 1064 nm. The device, which uses a multigrating MgO:PPLN crystal
for OPO and a MgO:sPPLT crystal fanout grating for intracavity SHG, provides cw single-frequency radiation tunable across 775–807 nm, with >3.0 W of
output across 56% of the tuning range, together with >3.8 W of mid-infrared
power over 77% of the idler tuning range of 3125–3396 nm for 27.4 W of fiber
pump power.
5.2
Experimental setup
The schematic of the experimental setup is shown in Fig. 5.1. The pump
source is a cw Yb-fiber laser (IPG Photonics, YLR-30-1064-LP-SF), delivering
up to 30 W of output power at 1064 nm in a single-frequency, linearly-polarized
beam with M 2 ∼1.01 and a nominal linewidth of 89 kHz. The nonlinear crystal used for OPO is a 48-mm-long, 6.2-mm-wide, 1-mm-thick, multigrating
MgO:PPLN sample (HC Photonics, Taiwan). The crystal contains five gratings with periods ranging from Λ=29.5–31.5 µm, in steps of 0.5 µm, with the
end faces antireflection (AR)-coated over 1450–1750 nm (R<1%), 2500–3700
nm (R<3%) and 1064 nm (R<3%). For intracavity SHG, we used 30-mm-long,
16-mm-wide, 0.5-mm-thick, MgO:sPPLT crystal (HC Photonics, Taiwan) with
96
5.2. Experimental setup
fanout grating, Λ=19.6–22.3 µm, across the 16 mm width. The crystal end
faces are AR-coated over 1500–1600 nm (R<1%) and 750–800 nm (R<1%).
The crystals are housed in two ovens with stability of 0.1o C, which can be controlled independently from room temperature to 200 o C. The OPO cavity is
configured in a folded ring, comprising four concave mirrors, M1−4 (r=150 mm)
and two plane mirrors, M5,6 . All mirrors (Laseroptik, Germany) are highly
reflective (R>99.6%) for the signal (1250–1800 nm) and highly transmitting
(T >90%) for the idler (2200–4000 nm), ensuring SRO operation. Mirror M4
is also highly transmitting (T >97%) over 600–800 nm. A lens of focal length,
f =200 mm, was used to focus the pump beam to a waist radius of w p =66 µm,
corresponding to confocal focusing parameter of ξ p ∼0.87, while the design of
the SRO cavity resulted in a primary signal waist radius of w s1 =80 µm at
the center of the MgO:PPLN crystal (bp ∼bs1 ) between mirrors M1 and M2 ,
and secondary signal radius of w s2 =117 µm (ξ s2 ∼0.26) at the center of the
MgO:sPPLT crystal, between mirrors M3 and M4 . Dichroic mirrors, M0 and
M00 , were used to separate the pump from the generated idler beam through
M2 , and the generated SHG beam from the leaked-out signal through M4 ,
respectively.
Figure 5.1: Schematic of the intracavity frequency-doubled cw OPO. FI: Faraday isolator,
λ/2: Half-wave plate, PBS: Polarizing beam-splitter, L: lens, M1−6 : Cavity mirrors, M0 and
M00 : Dichroic mirrors.
Chapter 5. All-periodically-poled, tunable, cw, near-infrared source
97
Photograph of the intracavity frequency-doubled cw OPO system operating
in our laboratory is shown in Fig. 5.2. The resonator mirrors and nonlinear
crystals are marked in accordance with the schematic of the experimental
configuration as shown in Fig. 5.1.
Figure 5.2: Photograph of the all-periodically-poled, near-infrared source operating in our
laboratory.
5.3
5.3.1
Results and discussion
Power across the tuning range
In this work, we used the Λ=30.5 µm grating period in the MgO:PPLN crys-
98
5.3. Results and discussion
tal, providing a signal tuning range of ∼1544–1618 nm and an idler range of
∼3423–3107 nm, for a change in the crystal temperature from 25 o C to 200 o C.
We initially varied the temperature of the MgO:sPPLT crystal (T SHG ) keeping
the crystal fixed at the longer grating periods, while maintaining the temperature of the MgO:PPLN crystal (T OP O ) at 177 o C (λsignal =1602 nm). At a
fixed pump power of 27.4 W, we measured the QPM temperature for SHG to
be 129 o C, confirming the longer grating period under use to be ΛSHG =22.12
µm.
Figure 5.3: Variation of SHG power as a function of SHG wavelength.
The SHG tuning in the present device can be achieved by varying the grating
period or temperature of the MgO:sPPLT crystal, while keeping either parameter fixed. Initially, SHG coverage across 775–801 nm was achieved by simultaneously varying temperature of MgO:PPLN crystal, T OP O , over 57 o C–177
o
C, and the grating period of MgO:sPPLT (ΛSHG ), at a fixed MgO:sPPLT
temperature of T SHG =129 o C. The SHG tuning range was then further extended up to 807 nm by increasing T OP O to 195 o C, for a fixed ΛSHG =22.12
µm, with corresponding increase in T SHG from 129 o C to 200 o C. This resulted
in an overall idler tuning over 271 nm, across 3125–3396 nm, corresponding to
a resonant signal wavelength range of 1550–1613 nm, and tunable SHG coverage over 775– 807 nm. Figure 5.3 shows the measured SHG power across the
tuning range for a fixed pump power of 27.4 W. As evident, the SHG is continuously tunable over the entire tuning range, providing >3 W of output power
Chapter 5. All-periodically-poled, tunable, cw, near-infrared source
99
over 56% of the SHG tuning range with a maximum of 3.7 W at λSHG =793
nm. Figure 5.4 shows the calculated SHG tuning curves, (a) and (b), using
the relevant Sellmeier equations [102], where good agreement with the experimental data in Fig. 5.3 has been confirmed. The simultaneously measured
idler power across the tuning range is shown in Fig. 5.5. We achieved >3.8 W
of output power over 77% of the idler tuning range with a maximum of 4.3 W
at λidler =3133 nm. The pump depletion remains above 61% over 67% of the
idler tuning range, and follows the similar behavior to the idler power over the
entire tuning range, as shown in Fig. 5.5.
Figure 5.4: Theoretical SHG (a) grating tuning range and (b) temperature tuning range in
present setup.
Figure 5.5: Variation of idler power and corresponding pump depletion across the idler
tuning range.
5.3.2
Power scaling
In order to investigate the performance of the device near 800 nm, we per-
100
5.3. Results and discussion
formed simultaneous power scaling measurements of SHG output and the corresponding idler at the SHG wavelength of 801 nm, as shown in Fig. 5.6(a).
The SHG power shows quadratic dependence up to ∼17 W of pump power,
beyond which it grows linearly, with a maximum of 3.2 W generated for 27.4
W of pump power. The corresponding maximum idler power obtained is 4.1
W at λidler =3168 nm, representing a total extraction efficiency of 26.6%. We
obtained the maximum overall extraction efficiency of 28% at a SHG wavelength of 793 nm, which corresponds to SHG power of 3.7 W together with
an idler power of 4.0 W at 3232 nm. The pump power threshold of the cw
SRO with intracavity SHG is recorded to be 7.5 W. The corresponding pump
depletion reaches a maximum of ∼65% at 24.6 W of pump power, as shown in
Fig. 5.6(a).
Figure 5.6(b) shows the variation of the signal power leaked-out through
mirror M4 , as a function of pump power. The signal power has a linear dependence on pump power up to ∼17 W, beyond which there is evidence of
saturation. The effect of saturation at higher pump power could be attributed
to the non-optimal mode matching. Considering the signal leakage through
other OPO cavity mirrors as well, we expect a total signal output power of
∼370 mW at maximum pump power. Using the leaked-out signal power and
transmission of mirror M4 at 1602 nm, we calculated the intracavity signal
power at maximum pump power to be 23.5 W, resulting in a single-pass SHG
conversion efficiency of 13.6%.
5.3.3
Power stability
We also recorded the passive power stability of the generated SHG at 801 nm
and the corresponding idler, simultaneously, for the maximum pump power of
27.4 W, under free-running conditions. The results are shown in Figs. 5.7(a)
and 5.7(b), where the SHG power is recorded to exhibit passive rms stability
Chapter 5. All-periodically-poled, tunable, cw, near-infrared source
101
Figure 5.6: Variation of (a) SHG power, idler output power, pump depletion, and (b) signal
power as a function of pump power.
102
5.3. Results and discussion
better than 3.5%, while the idler power stability is recorded to be better than
1.3% over more than 1 minute. The power stability of the system is expected to
be improved with active control, and using thermal and mechanical-vibration
isolation.
Figure 5.7: Simultaneously recorded passive power stability of (a) SHG and (b) idler output
from the SRO.
5.3.4
Single-frequency operation and beam quality
Further, we analyzed the single-frequency spectrum of the SHG output using
a confocal Fabry–Perot interferometer (FSR=1 GHz, finesse=400). The measurement was performed at 801 nm and at maximum SHG power. The transmission spectrum confirms single-frequency operation with an instantaneous
linewidth of 8.5 MHz, as shown in Fig. 5.8. Similar behavior was observed
across the full SHG tuning range.
Figure 5.9 shows the recorded far-field energy distribution of the SHG output at 801 nm, together with the orthogonal intensity profiles, at maximum
pump power. The data confirm Gaussian distribution with a beam circularity
>90%. For different pumping levels, and across the tuning range, we have
observed similar behavior. We measured the M 2 factor of the SHG beam at
Chapter 5. All-periodically-poled, tunable, cw, near-infrared source
103
maximum pump power using a lens and scanning beam profiler, and found
M x 2 <1.4 and M y 2 <1.4, confirming TEM00 spatial mode.
Figure 5.8: Single-frequency spectrum of generated SHG at 801 nm for pump power of 27.4
W.
Figure 5.9: Far-field energy distribution of generated SHG at 801 nm for pump power of
27.4 W.
5.4
Conclusions
In conclusion, we have demonstrated a high-power, single-frequency, highbeam-quality, cw source tunable across 775–807 nm using intracavity frequencydoubling of a cw SRO based on all-periodically-poled materials. Together with
SHG, idler tuning across 3125–3396 nm has also been achieved, providing high
104
5.4. Conclusions
output power. With improved thermal isolation and active control, the power
stability could be further improved. The SHG tuning can be further extended
to cover almost the entire Ti:sapphire wavelength range (∼740–972 nm) using
different grating periods of the employed MgO:PPLN crystal and simultaneously varying the grating of the MgO:sPPLT crystal. In order to further extend
the tunability in signal wavelength range, partial signal output coupling can be
implemented [41, 103], but at the cost of lower output SHG power. Given the
power scaling capability of fiber lasers, the described approach also offers clear
potential for even higher SHG output powers with increased pump powers.
Chapter 6
Continuous-wave ultraviolet
source based on BiB3O6
This chapter constitutes the following publication:
1. Stable, continuous-wave, Yb-fiber-based single-pass ultraviolet source
S. Chaitanya Kumar, K. Devi, and M. Ebrahim-Zadeh
Opt. Letters, submitted (2013)
6.1
Motivation
Continuous-wave (cw) ultraviolet (UV) sources are of great interest for variety
of applications including photolithography, optical data storage, flow cytometry and other life science applications. For many years, access to the UV
spectral region was possible mainly by bulky, complex and power-hungry gas
lasers [104].
Type-0 (eee)
Birefringent
3 -order QPM
BIBO
MgO:sPPLT
rd
Type-I (eeo)
Birefringent
BBO
Noncritical
θ=146.2o , φ=90o
θ=31
o
θ=90o , φ=37.2o
PM angle
2.7
0.67
2.42
0.87
2.0
3.9
0.12
FOM
0.7
def f (pm/V)
<1
0.02 (o-ray)
<0.1
0.003
@ 355 nm
αU V (cm−1 )
Table 6.1: Phase-matching (PM) properties of some nonlinear crystals for UV generation.
Type-I (ooe)
Type-I (ooe)
Birefringent
LBO
Type/ Interaction
PM
Crystal
–
3.23
0
0
∆ρ (mrad)
106
6.1. Motivation
Chapter 6. Continuous-wave ultraviolet source based on BiB3 O6
107
With the advent of nonlinear materials such as LiB3 O5 (LBO) and βBaB2 O4 (BBO), optical frequency conversion proved an attractive alternative
to reach the UV wavelength range, even enabling recent commercial realization
of all-solid-state cw UV sources. Owing to the relatively small nonlinearity of
LBO and BBO, as well as the low nonlinear gain available in the cw regime,
such sources typically employ intracavity sum-frequency-generation (SFG) or
cascaded second-harmonic-generation (SHG) in external resonant enhancement cavities, both requiring complex system architectures and mandatory
active stabilization. On the other hand, single-pass schemes are simple, compact and robust, and can directly transfer the frequency and power stability of
the input to the frequency converted output without the need for active stabilization. However, the material of choice should possess sufficiently high nonlinearity to generate practical output powers. Hence, the choice of the nonlinear material is very crucial for efficient UV generation in a single-pass scheme.
The phase-matching (PM) properties of some promising nonlinear materials for
UV generation are listed in Table 6.1. The most widely established materials
for UV generation are birefringently phase-matched LBO [105] and BBO [106],
but their low nonlinearity precludes single-pass SFG. The quasi-phase-matched
(QPM) nonlinear material such as MgO-doped periodically-poled stoichiometric LiTaO3 (MgO:sPPLT) with high nonlinearity and no spatial walk-off, also
has wide transparency range into the UV. It has been successfully deployed
in single-pass SHG configuration to generate high-power cw single-frequency
green radiation [44, 74, 107]. However, 1st -order QPM SFG into the UV requires a grating period of ∼2 µm, which is quite challenging to fabricate.
As a result 3rd -order QPM, with a reduced effective nonlinear coefficient of
2.7 pm/V has been used to generate UV radiation under temperature phasematching [108, 109]. On the other hand, the birefringent material, BiB3 O6
(BIBO), belonging to the borate family of nonlinear crystals, possesses unique
linear and nonlinear optical properties for frequency conversion from the UV
108
6.2. Experimental setup
to the infrared [110–112]. It can be phase-matched, at room temperature for
UV generation under type-I (ee→o) interaction for SFG of infrared and green.
As the two input beams at 1064 nm and 532 nm are extraordinarily polarized,
they experience a spatial walk-off of 64.8 mrad and 68 mrad, respectively, corresponding to a small relative walk-off, ∆ρ∼3.2 mrad. Its high nonlinearity
(d ef f ∼3.9 pm/V) [111], bulk UV damage threshold (50 MW/cm2 ) [113] and
low UV absorption coefficient (αU V <0.02 cm−1 ) [110, 111] makes it an attractive alternative material for SFG into the UV. Its nonlinear figure-of-merit,
FOM is >20 times higher as compared to that of LBO. As such, BIBO offers
a highly attractive material for cw UV generation using SFG of 1064 nm and
532 nm radiation.
In this chapter, we demonstrate this capability in a single-pass SFG scheme,
and in a fiber-based format, by using a cw Yb-fiber laser at 1064 nm as the
input pump source. By deploying MgO:sPPLT as the SHG crystal [44, 107]
and BIBO for SFG, up to 68 mW of cw UV single-frequency radiation at 354.7
nm has been generated. The generated UV output exhibits a passive power
stability better than 3.2% rms over 2 hours and frequency stability better than
437 MHz over >2.5 hours, in a TEM00 spatial beam profile. To our knowledge,
this is the first demonstration of fiber-based single-pass cw SFG into the UV
using BIBO.
6.2
Experimental setup
The schematic of experimental setup for single-pass UV generation is shown in
Fig. 6.1. The fundamental pump source is a cw Yb-fiber laser (IPG Photonics, YLR-30-1064-LP-SF) delivering up to 30 W of output power at 1064 nm
in a single-frequency, linearly-polarized beam with M 2 ∼1.01 and a nominal
linewidth of 89 kHz. An isolator at the output end of the fiber protects the
laser from any back-reflections. The power from the fiber laser is adjusted by
Chapter 6. Continuous-wave ultraviolet source based on BiB3 O6
109
using a combination of half-wave plate (HWP) and polarizing beam-splitter
(PBS) cube. A second HWP is used to obtain the required polarization for
phase-matching in the nonlinear crystal. The setup essentially consists of a
SHG stage and a SFG stage. We used a 30-mm-long, 2-mm-wide and 1-mmthick MgO:sPPLT crystal with a single grating period of 7.97 µm, housed
in an oven with a temperature stability of ±0.1 o C, for the SHG stage. The
SFG stage comprises a 10-mm-long, 3-mm-wide and 3-mm-thick BIBO crystal,
cut at θ=146.3o and φ=90o for type-I (ee→o) phase-matched sum-frequencymixing of 1064 and 532 nm radiation to generate UV radiation at 354.7 nm.
The SHG stage is temperature phase-matched, while the SFG stage is angular
phase-matched. The end faces of both the crystals are antireflection (AR)coated (R<1%) at 1064 nm and 532 nm, while BIBO is also AR-coated for
high transmission at 354.7 nm. Using a lens of focal length, f =125 mm, the
fundamental beam at 1064 nm is focused to a waist radius of w F 1 ∼30 µm
at the center of the MgO:sPPLT crystal for SHG into the green at 532 nm.
The generated green and the undepleted fundamental are again collimated and
refocused by using, M1 and M2 in the SFG stage [44, 107]. The angle of incidence on these mirrors is limited by the mechanical constrains and are kept as
small as possible. All the concave mirrors are AR-coated for high reflectivity
(R>99%) at 1064 nm and 532 nm and are mounted on translation stages, so
as to adjust the inter-crystal spacing. The radius of curvature of M1 and M2
are 150 mm and 200 mm, respectively, resulting in an estimated fundamental
and generated SHG beam waist radii of w F 2 ∼43 µm and w SHG2 ∼30 µm at the
center of the BIBO crystal, corresponding to a Rayleigh range of >1 cm for
both the beams. Rayleigh range, considering the refractive index of BIBO, is
∼2 cm in both the cases. It is well-known that in order to achieve effective
interaction, the two beams must have same Rayleigh range [76]. In practice,
optimum efficiency for SFG is achieved when the two interacting beam overlap as much as possible through the length of the crystal. The generated
110
6.2. Experimental setup
UV radiation is separated using dichroic mirrors, M, and a piece of Scott glass
(UG-11), F is used to filter out any residual fundamental and second-harmonic
while measuring UV power. Figure 6.2 shows the picture of the single-pass UV
generation setup operating in our laboratory, where the mirrors and nonlinear
crystals are marked. The picture of the generated UV beam is also shown.
Figure 6.1: Schematic of experimental setup for the fiber-laser-based single-pass UV source.
FI: Faraday isolator, λ/2: Half-wave plate, PBS: Polarizing beam-splitter, L: Lens, M:
Mirrors, F: Filter.
Figure 6.2: Picture of the cw UV source operating in our laboratory (left) and the generated
UV beam (right).
Chapter 6. Continuous-wave ultraviolet source based on BiB3 O6
6.3
6.3.1
111
Results and discussion
Power scaling
In order to characterize our UV source, we performed the power scaling measurement of the generated UV radiation at the output of the SFG stage. Figure
6.3 shows the variation of single-pass UV power generated in BIBO as a function of input fundamental power to the SHG stage, where it can be seen that
we achieved as much as 68 mW of UV power at 354.7 nm for a fundamental
power of 27.8 W at 1064 nm. During the measurements, as the fundamental
power is increased, the phase-matching temperature of MgO:sPPLT crystal is
always adjusted to generate maximum UV power. Also shown in Fig. 6.4 is
the power and efficiency scaling measurement of single-pass SHG at 532 nm, in
MgO:sPPLT crystal. While generating maximum UV power, the SHG power
is recorded to be 8.2 W at the input to the SFG stage. At higher fundamental
powers beyond 20 W, SHG efficiency is observed to be saturated providing
a maximum SHG efficiency of 29%. The ratio of SHG to the fundamental
power varied from 0 to 0.3 during the UV power scaling measurement. In
order to study the effect of SHG to fundamental power ratio, we changed the
temperature of the MgO:sPPLT crystal away from optimum phase-matching
condition, thereby reducing the SHG power and increasing the undepleted fundamental, while pumping at the maximum available fundamental power of 27.8
W. However, we found that UV power is always maximized when the SHG is
maximum, indicating that the generated UV power is limited by the available
SHG power. Further, fixing the phase-matching temperature at its optimum
value to generate maximum SHG power, and pumping beyond 20 W of fundamental power, we found that the generated UV power is strongly affected
by the depletion in the fundamental power, resulting in a >5% drop in the
UV power associated with fundamental beam quality degradation, which soon
reached a stable, steady state condition with no further reduction in the out-
112
6.3. Results and discussion
put UV power. Under certain conditions we were able to generate UV power
>70 mW, however it was not stable.
Figure 6.3: Variation of the cw UV power as a function of fundamental power at the output
of the SFG stage.
Figure 6.4: Dependence of the measured cw SHG power and the corresponding conversion
efficiency on the incident fundamental power at the output of SHG stage.
6.3.2
Power stability and spectrum
After continuous operation of the UV source over >10 hours at maximum
fundamental power, we observed a ∼30% drop in the UV power, which could
Chapter 6. Continuous-wave ultraviolet source based on BiB3 O6
113
be retrieved by translating the BIBO crystal, to use a new portion of the
crystal. This drop in the output UV power is attributed to the AR-coating
damage on the exit face of the BIBO crystal which was also previously observed
in well-established materials such as LBO [114]. Further studies are necessary
to understand the origin of this damage. In order to avoid any further damage
to the BIBO crystal, we limited the UV power to ∼50 mW with reduced
fundamental power in the rest of our measurements.
We have recorded the long-term power stability of the generated UV at ∼50
mW of output power. The results are presented in Fig. 6.5, where it can be seen
that the UV output exhibits a passive power stability better than 3.2% rms
over 2 hours and 1.5% rms over 50 minutes. Also shown in the inset of Fig. 6.5
is the spectrum of the generated UV radiation centered at 354.7 nm, measured
using a spectrometer with a resolution of 0.27 nm (OceanOptics, HR4000).
As the fundamental and the SHG are measured to be single-frequency with a
linewidth of 89 kHz and 6.5 MHz, respectively, it is expected that the generated UV is also single-frequency. However, we were not able to measure the
linewidth of the UV output due to a lack of suitable optics for our Fabry-Perot
interferometer.
6.3.3
Frequency stability and beam quality
In order to study the frequency deviation of our single-pass UV source, we
recorded the output wavelength as a function of time. The frequency stability
of the generated UV radiation, measured at ∼50 mW of output power using
a wavemeter (High finesse, WS/U-30) with a resolution of 5 MHz, is shown
in Fig. 6.6. Under free-running conditions and in the absence of thermal
isolation, the UV output exhibits a peak-to-peak frequency deviation <437
MHz over the >2.5 hours, measured at a central wavelength of 354.7945 nm.
The far-field energy distribution of the UV beam at 354.7 nm, together
114
6.3. Results and discussion
Figure 6.5: UV output power stability at 50 mW over >2 hours. Inset: UV spectrum
measured at maximum output power.
Figure 6.6: Long-term frequency stability of the generated UV output at 354.7945 nm, over
a period of >2.5 hours.
Chapter 6. Continuous-wave ultraviolet source based on BiB3 O6
115
with the intensity profiles and the Gaussian fits along the two orthogonal
axes measured at the output of the SFG stage are shown in Fig. 6.7. The
UV beam exhibits an ellipticity of 66% due to the spatial walkoff between
the fundamental, green and UV beams, but can be readily circularized using
suitable cylindrical optics. In order to confirm a Gaussian distribution, we
measured the M 2 factor of the UV beam at the highest available fundamental
power, using a f =100 mm focusing lens and scanning beam profiler, resulting
in M x 2 <1.6 and M y 2 <1.8, indicating a TEM00 spatial mode.
Figure 6.7: Far-field energy distribution and intensity profiles of the generated UV beam at
maximum output power.
6.4
Conclusions
In conclusion, we have demonstrated for the first time, a compact Yb-fiberlaser-pumped cw UV source based on BIBO using single-pass SFG of fundamental at 1064 nm and second-harmonic radiation at 532 nm generated by
1st -order QPM interaction in MgO:sPPLT. The cw UV source provides as
much as 68 mW of single-frequency power at 354.7 nm with a passive stability better than 3.2% rms over 2 hours and frequency stability better than
437 MHz over >2.5 hours in an elliptic TEM00 spatial mode with M x 2 <1.6
and M y 2 <1.8, which can be readily improved using suitable cylindrical beam
shaping optics. The practical output power and compact fiber-based design
116
6.4. Conclusions
together with high stability and good beam quality make the device viable
source of cw UV radiation for many applications.
Chapter 7
Dual-wavelength, ARR-coupled,
cw OPO
This chapter constitutes the following publication:
1. Dual-wavelength interferometrically-coupled continuous-wave optical para-
metric oscillator
K.Devi, S. Chaitanya Kumar, A. Esteban-Martin,
and M. Ebrahim-Zadeh
Laser and Photonics Reviews, submitted (2013)
7.1
Motivation
For many scientific and technological applications such as spectroscopy, frequency metrology, differential absorption lidar, and nonlinear frequency conversion, high-power coherent dual-wavelength light sources are of great interest. In particular, the ability to produce two closely spaced tunable wavelengths is important for generation of terahertz radiation [29,115,116]. Optical
parametric oscillators (OPOs) are well-established coherent sources, capable
118
7.1. Motivation
of providing tunable wavelengths from the ultraviolet to mid-infrared [5]. The
generated wavelengths in an OPO are determined simultaneously by energy
conservation and phase-matching conditions. Thus, in a conventional OPO,
the closest signal and idler wavelengths can be generated only near degeneracy,
but in practice this is challenging due to instabilities associated with double
resonance. On the other hand, away from degeneracy, signal and idler pairs
with arbitrary wavelengths cannot be generated, due to the constraints imposed by energy conservation and phase-matching. In order to overcome these
limitations, various schemes based on dual-crystal parametric amplification,
double-pass in a single crystal and pump-enhanced OPO have been reported
earlier [115, 116]. However, these configurations suffer from drawbacks such
as pump beam quality degradation affecting the efficiency, thermal effects and
damage to the nonlinear crystal. Recently, to overcome these limitations, a
dual-wavelength continuous-wave (cw) OPO using two nonlinear crystals has
been reported, generating signal (idler) pairs with frequency separation down
to 0.55 THz. In this scheme, the minimum wavelength separation is limited
by the parametric gain overlap of the nonlinear crystals [117]. As such, one
may also consider alternative approaches that would avoid coherent coupling
between the two resonant waves in close proximity, thus permitting the generation of signal (idler) wavelength pairs with indefinitely close separation.
In this chapter, we demonstrate such a technique by using an antiresonant
ring (ARR) interferometer to couple two cw OPO cavities. Recently, such an
approach has been demonstrated in femtosecond OPOs [118]. In cw regime,
we have demonstrated the use of the ARR interferometer for optimum output coupling [103], as discussed in chapter 4, and mode-locking [119], which
will be discussed in section 8.1. Here, we demonstrate the use of the ARR
interferometer for dual-wavelength generation in cw OPOs, for the first time,
providing two distinct signal (idler) wavelength pairs that can be independently
and arbitrarily tuned to indefinitely close separation, through degeneracy, and
Chapter 7. Dual-wavelength, ARR-coupled, cw OPO
119
beyond. Using two cw singly-resonant OPOs connected with a common ARR
interferometer, we generate signal waves with frequency separation of 0.8 THz,
limited by measurement and show their overlap at 951 nm. The architecture
provides high intracavity power at both signal waves within the ARR, while
avoiding coupling between the two circulating fields.
7.2
Experimental setup
The configuration of ARR-coupled cw OPO is shown in Fig. 7.1. The single
pump source used in the experiment is frequency-doubled, diode-pumped cw
Nd:YVO4 laser (Coherent, Verdi V-10), delivering up to 10 W of output power
at 532 nm in a single-frequency, linearly-polarized beam with M 2 <1.1. The
pump radiation is divided into two beams (P1 and P2 ), using a combination of a
half-wave plate (H1 ) and a polarizing beam-splitter (PBS), and the two beams
then separately pump two OPOs (OPO-1 and OPO-2). The half-wave plates,
H2 and H3 , are used to control the pump polarization for phase-matching in
the two nonlinear crystals, X1 and X2 . The crystals are identical 30-mm-long
MgO:sPPLT, each with a single grating period of Λ=7.97 µm. They are housed
in separate ovens, whose temperature can be controlled from room temperature
to 200 o C with a stability of ±0.1 o C. The crystal faces are antireflection-coated
(R<0.5%) over 850–1064 nm, with high transmission (T >98%) at 532 nm. The
residual reflectivity of the coating over the idler range of 1064–1400 nm is 0.5%–
15%. Using two identical lenses, L1 and L2 (f =150 mm), we focused the pump
beams to waist radii, w p1 ∼w p2 ∼31 µm, at the center of X1 and X2 . The OPO-1
is configured in a standing-wave cavity comprising two concave mirrors, M1 and
M2 , with an ARR in the folded arm. The ARR consists of a beam-splitter (BS)
and two plane mirrors, M3 and M4 . The OPO-2 is also configured in standingwave cavity identical to OPO-1, using two concave mirrors, M5 and M6 , and
shares the same ARR incorporated in the folded arm. However, unlike OPO-
120
7.2. Experimental setup
1, in order to integrate the ARR into OPO-2, we used three additional plane
mirrors, M7−9 in the folded arm. All mirrors were highly reflecting for the signal
(R>99.7% @ 840-1020 nm), and transmitting for the pump (T >98% @ 532
nm) and idler (T >97% @ 1100-1400 nm), thus ensuring single-pass pumping
and singly-resonant signal oscillation in both OPOs. The total cavity length
of OPO-1 is LOP O−1 =106.6 cm, which is the sum of the standing-wave cavity
length (2Llinear−1 =2x45.5 cm) and the length of the ARR (Lring =15.6 cm),
while for OPO-2 it is LOP O−2 =2Llinear−2 +Lring =112.6+15.6=128.2 cm. The
BS is a UV fused silica plate (12.5-mm-diameter, 3-mm-thick) with broadband
coating over 700–1100 nm, available in our laboratory The alignment of the
ARR is similar to that demonstrated in chapter 4, except that here, in order to
couple the two OPOs while avoiding any perturbation in one due to the other,
we arrange the incident angle (θBS ) on the BS for near-zero output coupling.
Thus, the ARR behaves as two interlaced, but independent mirrors, highly
reflecting at signal wavelength for both OPOs.
Figure 7.1: Experimental setup of the ARR-coupled cw OPO. H1−3 : Half-wave plates,
PBS: Polarizing beam-splitter, P1 , P2 : Pump beams, L1,2 : Lens, M1−9 : Cavity mirrors,
X1,2 : MgO:sPPLT crystals, M: Dichroic mirrors, BS: Beam-splitter, λ1s , λ2s : Dual signal
wavelengths leaked through M3 , I1,2 : Idler beams.
Chapter 7. Dual-wavelength, ARR-coupled, cw OPO
121
Photograph of the ARR-coupled cw OPO system operating in our laboratory is shown in Fig. 7.2. The resonator mirrors, nonlinear crystals, OPO-1,
OPO-2, and ARR interferometer are marked in accordance with the schematic
of the experimental configuration as shown in Fig. 7.1.
Figure 7.2: Picture of the ARR-coupled cw OPO operating in our laboratory.
7.3
7.3.1
Results and discussion
Charaterization of the ARR interferometer
To determine near-zero output coupling angle for the BS, we initially characterized the ARR externally. As the 1st surface of BS faces OPO-1 and 2nd
surface faces OPO-2, we performed the characterization consecutively in both
directions, as perceived by the signal beams from the two OPOs. We measured the input power to the ARR and the output power from the ARR at
different angles, θBS , and calculated the transmission of the ARR, T ARR , at
a fixed signal wavelength of 951 nm. Figure 7.3 shows the ARR transmission
as a function of θBS for both BS surfaces. With the 1st surface, the transmission remains minimum (T ARR =0.3%) at smaller angles of 5o <θBS <15o .
With further increase of θBS beyond 15o , T ARR increases to 3.3% at θBS =35o .
The transmission of the ARR with input from the 2nd surface at large angles
122
7.3. Results and discussion
(θBS >25o ) is qualitatively the same as that with input from the 1st surface.
However, in this case, the minimum transmission was measured to be 0.7%
for angles 5o <θBS <15o . The difference in the ARR transmission is attributed
to the broadband coating only on the 2nd surface of the BS. Thus, we fixed
θBS =12o for minimum transmission through both surfaces and incorporated
the ARR inside OPO-1 and OPO-2.
Figure 7.3: Transmission of the ARR interferometer as a function of BS angle.
Figure 7.4 shows the direction of signal waves from OPO-1 and OPO-2, and
within the ARR. As seen, the architecture provides high intracavity powers for
both resonant wavelengths in the same direction, inside the ARR.
7.3.2
Tuning capability of ARR-coupled cw OPO
We optimized OPO-1 and OPO-2 to achieve equal idler powers of >1W, while
pumping simultaneously with pump power of 4.3 W and 5.7 W, respectively.
In order to demonstrate versatile tuning capabilities of the ARR-coupled cw
OPO, we systematically temperature tuned each OPO and recorded the spectrum of the signal leaking through the ARR mirror (M3 ), where high-power,
dual-wavelength operation is expected. OPO-1 is temperature tuned from
Chapter 7. Dual-wavelength, ARR-coupled, cw OPO
123
Figure 7.4: Direction of the dual wavelength signal beams to and from the OPOs, and within
the ARR.
T1 =110 o C down to 90 o C, while OPO-2 is tuned from T2 =90 o C up to 110
o
C. The results are shown in Fig. 7.5. As evident, this systematic variation of
the temperature enables smooth and continuous tuning of the resonant signal
wavelengths with a frequency difference from 6.6 THz, indefinitely down, until
they completely overlap and tune through degeneracy, up to 7 THz. At T1 =102
o
C (λ1s =949.9 nm) and T2 =98 o C (λ2s =952.5 nm), the difference between the
resonant signal frequencies is as low as 0.8 THz, limited by the measurement
with the spectrometer. The frequency difference is further reduced by decreasing T1 towards 101 o C and increasing T2 towards 100 o C, finally leading to
two identical resonant signal wavelengths at 951 nm (T1 =101 o C, T2 =100 o C)
oscillating independently in each OPO. The 1 o C difference in crystal temperatures to generate the same signal wavelength is mainly due to the small
difference in the design and calibration of the two ovens. Further decrease in
T1 and increase in T2 lead to the crossover of the resonant wavelengths from
the two OPOs, confirming arbitrary tuning enabled by the ARR coupling. As
seen, the frequency difference between the resonant waves then increases from
1.8 THz (T1 =98 o C, T2 =102 o C) to 7 THz (T1 =90 o C, T2 =110 o C).
124
7.3. Results and discussion
Figure 7.5: Signal spectra from the ARR-coupled, dual-wavelength OPO at independently
tunable crystal temperatures, T1 and T2 .
7.3.3
Single-frequency operation
Maintaining the crystal temperatures at T1 =101 o C and T2 =100 o C, we observed the spectrum of the resonant signal waves (λ1s =λ2s =951nm), leaked
through the same ARR mirror (M3 ), using a confocal Fabry-Perot interferometer (FSR=1GHz, finesse=400). The results are shown in Fig. 7.6. By
blocking P2 and operating OPO-1 at a pump power of 4.3 W, we recorded the
typical fringe pattern of the transmitted signal, confirming single-frequency
operation of OPO-1 with an instantaneous linewidth of ∼20 MHz. Similarly,
by blocking P1 and operating OPO-2 pumped at 5.7 W of pump power, we
confirmed single-frequency operation of OPO-2 with a linewidth of ∼20 MHz.
We further recorded the instantaneous transmission spectrum of both waves
together, using the same Fabry-Perot interferometer, and measured the frequency separation of ∼220 MHz between the two signal waves relative to each
Chapter 7. Dual-wavelength, ARR-coupled, cw OPO
125
other, as shown in Fig. 7.6. In order to confirm the isolation provided by the
ARR at degeneracy, we have measured the output power during simultaneous and individual operation of the OPOs. We have not observed any change
in the output idler power from the OPOs. Also, the threshold pump power
remains same.
Figure 7.6: Fabry-Perot transmission spectra of the dual signal wavelengths.
7.3.4
Power scaling
To show power scalability of the system, we measured the idler output power
as a function of input pump power for both OPOs when oscillating simultaneously, keeping T1 =101 o C and T2 = 100 o C. The results are shown in Fig.
7.7(a). For OPO-1, the idler power increases linearly up to a 4.5 W of pump
power, while for OPO-2 it is linear up to 5 W of pump, beyond which there
is slight evidence of saturation, which could be attributed to thermal effects,
pump depletion and backconversion. We achieved a maximum idler power of
1.6 W from OPO-1 for a pump power of 6.3 W, while OPO-2 is close to thresh-
126
7.3. Results and discussion
old using the remaining 3.7 W of pump. Similarly, 1.4 W of idler is generated
from OPO-2 for 7 W of pump power, with OPO-1 operating near threshold at
a pump power of 3 W. Further increasing the pump power to one OPO makes
the other OPO unstable until it finally ceases operation. OPO-1 and OPO-2
have an operation threshold power of 2.8 W and 3.2 W, respectively.
Figure 7.7: (a) Idler output power from OPO-1 and OPO-2 versus pump power, with both
OPOs in simultaneous operation. (b) Power scaling of OPO-2 without the ARR.
We also performed power scaling for both OPOs in the short v-cavity configuration by placing highly reflecting mirrors (at signal) in place of the ARR.
Each OPO without the ARR was configured with a cavity length of 63 cm.
Chapter 7. Dual-wavelength, ARR-coupled, cw OPO
127
Both OPOs without ARR showed similar performance, providing maximum
idler power of ∼2.3 W for a pump power of ∼10 W with an operation threshold
of ∼1.4 W. Figure 7.7(b) shows the power scaling results for OPO-2 without
the ARR. As evident, OPO-1 with the ARR incorporated in it shows similar
output power as that of the OPO without ARR, at same pump power. However, the lower output power from OPO-2 with the ARR incorporated is due
to the longer cavity length and additional mirrors (M7−9 ) used. Further, the
increase in threshold power for both OPOs with the ARR incorporated, as
compared to that of without ARR, is attributed to the additional losses due
to the ARR elements, which can be further reduced.
We also confirmed that the incorporation of the ARR did not have any
adverse effect on output beam quality, with the signal beam from both OPOs
exhibiting TEM00 spatial profile.
7.4
Conclusions
In conclusion, we have described a dual-wavelength, ARR-coupled, cw OPO
with signal (idler) wavelength pairs which can be independently and arbitrarily tuned through degeneracy and beyond. We have demonstrated frequency
separation from 7 THz down to ∼220 MHz at identical signal wavelengths,
although there is no limit to the minimum attainable wavelength separation,
even to exact degeneracy. Both circulating signal waves provide high intracavity power and narrow linewidth, making the technique particularly attractive
for efficient generation of widely tunable terahertz radiation, as well as other
potential applications. The approach can also be extended to other spectral
regions and operating time-scales.
Chapter 8
Mode-locked, cw OPOs
This chapter constitutes the following publications:
1. Frequency-modulation-mode-locked optical parametric oscillator
A. Esteban-Martin, G. K. Samanta, K. Devi, S. Chaitanya Kumar,
and M. Ebrahim-Zadeh
Opt. Letters 37, 115-117 (2012)
2. Mode-locked, continuous-wave, singly resonant optical parametric oscilla-
tor
K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh
Opt. Letters 37, 3909-3911 (2012)
3. Directly phase-modulation-mode-locked doubly-resonant optical paramet-
ric oscillator
K. Devi, S. Chaitanya Kumar, and M. Ebrahim-Zadeh
Opt. Express, submitted (2013)
8.1
Motivation
Since the first indication of mode-locking in ruby laser by Gurs and Muller
130
8.1. Motivation
[120], there has been tremendous development in the field of mode-locked
lasers in terms of mode-locking methods and understanding [57, 58]. For the
past few decades, generation of ultrashort pulses has been a primary source of
interest due to its manifold of applications in different areas such as material
processing, metrology, spectroscopy, optical microscopy, medical domain and
nonlinear frequency conversion processes [121, 122]. From active to passive,
many mode-locking methods have been exploited for short pulse generation.
However, except the Ti:sapphire laser [97, 123] known as the workhorse in
the ultrafast regime and the Yb-doped fiber laser, the mode-locked lasers still
suffer from the general lack of widespread availability and are tunable in particular wavelength regime only. Hence, efforts have been made to increase their
tunability and spectral coverage by deploying nonlinear frequency conversion
techniques. The optical parametric oscillators (OPOs) have indeed proved to
be a promising candidate towards this goal, as they are the viable sources
of widely tunable radiation for spectral regions inaccessible to lasers, operating in all time scales from continuous-wave (cw) to ultrafast femtosecond
domain. Due to the lack of gain storage, operation of OPOs in the ultrafast
picosecond and femtosecond regime has traditionally relied on the technique of
synchronous pumping by using mode-locked pump lasers and careful matching
of the OPO cavity length to the pump laser repetition rate. However, given the
high complexity and cost of the mode-locked lasers as compared to cw lasers,
the synchronous pumping approach often result in elaborate system design, increased cost and large size for ultrafast OPOs. It would be desirable, therefore,
to consider novel alternative methods for the development of ultrafast OPOs
that do not rely on synchronous pumping with mode-locked pump lasers. One
such technique could be direct mode-locking of cw OPOs. This approach could
enable the generation of tunable ultrashort pulses over wide spectral regions
using OPOs by deploying widely available cw pump lasers, thus circumventing
the need for ultrafast laser sources and synchronous pumping. Such an ap-
Chapter 8. Mode-locked, cw OPOs
131
proach was previously attempted in a doubly-resonant oscillator (DRO) under
quasi-cw pumping [47] using an acousto-optic modulator (AOM) as the active
mode-locking element, where steady-state pulses with nanosecond duration
were generated. Also, attempts were made under cw pumping using an AOM
in a ring-cavity singly-resonant oscillator (SRO), again providing nanosecond
pulses in steady-state operation [60].
In this chapter, we demonstrate for the first time, direct active mode-locking
of a cw OPO in both DRO as well as SRO configuration, generating picosecond
pulses. In section 8.3, we demonstrate a hybrid mode-locking technique based
on the use of an intracavity electro-optic phase modulator (EOM) in combination with an antiresonant ring interferometer (ARR), providing phase-toamplitude conversion, thus enabling ultrashort pulse generation. A cw DRO
has been used and operated near degeneracy to initiate broad signal-idler bandwidths. Using the technique, we generate 730 ps pulses at 160 MHz and 450
ps pulses at 80 MHz. In section 8.4, we demonstrate the direct active modelocking of the cw DRO, only by deploying intracavity phase modulation, without the use of an ARR interferometer, generating 533 ps pulses at 80 MHz
and 471 ps pulses at 160 MHz. In spite of the large spectral signal-idler bandwidths available under near-degeneracy operation, which could be desirable
for ultrashort pulse generation, cw DROs suffer from mode-hoping and nonmonotonous tuning, which ultimately limit stability in mode-locked operation.
On the other hand, cw SROs offer higher passive spectral, temporal, and output power stability, which could result in robust operation under mode-locking.
Because of their intrinsic frequency stability, the SROs can also be the favorable design when used together with resonant phase modulators, which are
specified for narrowband or single-frequency operation. The combination of
cw SRO together with a resonant phase modulator could thus potentially enable the generation of shorter pulses. Hence, it is worthwhile to explore direct
mode-locking of cw SROs using resonant phase modulation. In section 8.5, we
132
8.2. External charaterization of the EOM
demonstrate direct active mode-locking of a cw OPO in SRO configuration,
based on pure phase-modulation, using the EOM as the single mode-locking
element, generating stable pulses of 230 ps duration at 80 MHz repetition rate.
8.2
External charaterization of the EOM
For active mode-locking, in the context of lasers, phase modulators with different modulation frequencies have been used in the past [62, 124–129]. To
our knowledge, till date the lowest modulation frequency with EOM used as
a single mode-locker for direct active mode-locking is 100 MHz. The resonant
EOM (New Focus, Model 4003) used in the present work has central resonant
frequency of n=80 MHz with tunability of ±5 MHz, typical bandwidth of 0.81.6 MHz, and quality factor of 36. It is based on a 40-mm-long MgO:LiNbO3
electro-optic crystal with a clear aperture of 2 mm. It has both the faces antireflection (AR)-coated over 1–1.6 mm. In order to study the performance of
the EOM, we initially characterized the EOM individually and externally. An
Yb-doped fiber laser (IPG Photonics, YLR-30-1064-LP-SF), providing 30 W
of single-frequency, linearly-polarized radiation at 1064 nm has been used as
the input laser source to the EOM. With 1 W of input power, we observed the
single-pass output from the EOM in frequency domain and also in time domain at different modulation depth and modulation frequency. Figure 8.1(a)
and 8.1(b) shows the transmission spectrum of the single-pass output through
the EOM, measured using a confocal Fabry-Perot interferometer, FPI (Free
Spectral Range, FSR=1 GHz, finesse=400) for different modulation depth and
frequency, by keeping either of the parameter fixed, respectively. As seen in (i)
of Fig. 8.1(a), at minimum modulation depth, µ1 and resonant frequency of
ν=80 MHz, single-frequency spectrum is seen, with instantaneous linewidth of
4.6 MHz. With increase in modulation depth to µ2 in (ii), keeping ν constant,
the amplitude of the central frequency begins to fall and side bands appears
Chapter 8. Mode-locked, cw OPOs
133
on both sides of the central frequency. The amplitude of the side bands increases with increase in modulation depth to µ3 in (iii). With further increase
in modulation depth to µ4 in (iv), the central frequency starts disappearing,
with no central carrier frequency at maximum available modulation depth of
µ5 in (v). The modulator produces 2 side bands on either side of the central
frequency, with side band spacing of ∼80 MHz. The side band spacing has
been observed as independent of the modulation depth. Figure 8.1(b) shows
the effect of increase in modulation frequency with modulation depth kept
fixed at µ3 . It has been observed that at minimum modulation frequency of ν 1
in (i), the spectrum remains single-frequency with instantaneous linewidth of
4.7 MHz. However, as the modulation frequency is increased, prominent and
maximum side bands are seen at ν in (iii) with less significant side bands at
other frequencies (ν 2 , ν 3 and ν 4 ).
We also monitored the output from the EOM in time domain using an InGaAs photodetector (20 GHz, 18.5 ps) and a fast oscilloscope (3.5 GHz, 40
GS/s). It is to be noted that the modulation signal applied to the EOM using a RF driver is sinusoidal. At a modulation frequency of ν=80 MHz and
increasing the modulation depth from µ1 to µ4 , we have not observed any modulation in the output. However, keeping the modulation frequency fixed at ν
and increasing modulation depth further to the maximum, a slight modulation
at a repetition rate of 160 MHz and width of 3 ns has been observed.
We have further calculated the values of different modulation depth, which
is the optical phase shift induced by the EOM used. The amplitude of the
central carrier frequency is given by [J 0 (µ)]2 , where J 0 is the Bessel function
of zero order and argument µ is the optical phase shift or the modulation depth
[124]. The sidebands seen in Fig 8.1(a) for different modulation depth, shows
the Bessel function amplitudes, as shown in Fig. 8.2. Comparing the amplitude
of the central carrier frequency obtained from the transmission spectrum at
different modulation depth of EOM in Fig. 8.1(a), with the amplitude of
[J 0 (µ)]2 from the theoretical Bessel plot in Fig. 8.2, the modulation depth of
134
8.2. External charaterization of the EOM
Figure 8.1: Single-pass EOM output spectrum (a) at ν=80 MHz for different modulation
depth (µ1 <µ2 <µ3 <µ4 <µ5 ) of (i) µ1 (ii) µ2 (iii) µ3 (iv) µ4 (v) µ5 and (b) for fixed modulation
depth of µ3 at different modulation frequency (ν1 <ν2 <ν<ν3 <ν4 ) of (i) ν1 (ii) ν2 (iii) ν (iv)
ν3 (v) ν4 .
Chapter 8. Mode-locked, cw OPOs
135
µ1 , µ2 , µ3 , µ4 and µ5 has been calculated to be 0, 1.63, 1.83, 1.99 and 2.4
radians, respectively.
Figure 8.2: Bessel function amplitude of order 0, 1, 2 and 3, representing the amplitudes
of carrier frequency, 1st , 2nd , and 3rd side bands, respectively, with modulation depth as
argument.
8.3
8.3.1
Mode-locking of cw DRO using ARR interferometer
Experimental setup
The schematic of the experimental setup is shown in Fig. 8.3. The fundamental pump source used is frequency-doubled, diode-pumped cw Nd:YVO4
laser (Coherent, Verdi V-10), delivering up to 10 W of output power at 532
nm in a single-frequency, linearly-polarized beam with M 2 <1.1. To maintain
stable laser output characteristics, we operated the pump laser at maximum
power and used a combination of a half-wave plate (HWP) and a polarizing
beam-splitter (PBS) cube as power attenuator. A second HWP was used to
adjust the pump polarization relative to the crystal orientation. The nonlinear
crystal is 30-mm-long MgO:sPPLT with a single grating period of 7.97 µm,
housed in an oven with a temperature stability of ±0.1 o C. The crystal faces
136
8.3. Mode-locking of cw DRO using ARR interferometer
are antireflection-coated (R<0.5%) over 850–1064 nm, with high transmission
(T >98%) at 532 nm. The residual reflectivity of the coating over the idler
range of 1064–1400 nm is 0.5%– 15%. Using a lens of focal length, f =150 mm,
the pump beam is focused to a waist radius of ∼31 µm (ξ∼1.2) at the center
of the crystal. The OPO cavity design ensures optimum overlap of pump and
resonant waves at the center of the crystal (bp ∼bs/i ), with a signal/idler waist
radius of ∼46 µm, where bp , bs/i are the confocal parameters of the pump
and signal/idler, respectively. The OPO is configured in a standing-wave cavity comprising two concave mirrors, M1 and M2 (r=100 mm), a plane mirror
(M3 ) in one arm, a concave mirror, M4 (r=1000 mm) and an ARR interferometer formed by two plane mirrors (M5 and M6 ) and a beam-splitter (BS)
integrated into the other arm. The EOM, described in section 8.2, is incorporated into the ARR. Mirror, M3 , is mounted on a translation stage to adjust
the length of the OPO, and the beam diameter through the aperture of the
EOM inside the ARR is adjusted using mirror M4 . All the mirrors are highly
transmitting (T >97%) for the pump and highly reflecting (R>99%) for the
signal and idler over 1000-1080 nm, thus ensuring DRO operation. The BS
is a UV fused silica plate (12.5-mm-diameter, 3-mm-thick) with a broadband
coating over 700–1100 nm. We arranged the incident angle (θBS ) on the BS for
minimum transmission from the ARR. The DRO is operated near degeneracy
by keeping the crystal temperature at 51.5 o C. The total optical length (LDRO )
of the DRO cavity including the linear arm, Llinear =143 cm, and ARR ring,
Lring =90 cm, when synchronized to the modulation frequency (ν=80 MHz)
of the EOM, is 3.7 m, where LDRO =2Llinear +Lring =c/ν, and c is the speed
of light. Figure 8.4 shows the picture of the mode-locked cw DRO operating in our laboratory, where the DRO cavity mirrors, ARR elements and the
nonlinear crystal are marked.
Chapter 8. Mode-locked, cw OPOs
137
Figure 8.3: Schematic of the continuous-wave, mode-locked DRO. λ/2: Half-wave plate,
PBS: Polarizing beam-splitter, L: Lens, M1−6 : Cavity mirrors, EOM: Electro-optic phase
modulator, BS: Beam-splitter.
Figure 8.4: Picture of the setup operating in our laboratory.
138
8.3.2
8.3. Mode-locking of cw DRO using ARR interferometer
Phase-to-amplitude modulation conversion
We performed external characterization of the ARR interferometer with the
EOM placed at the centre of the ARR between mirrors M5 and M6 , prior to
integration into the cw DRO. We operated the cw DRO near degeneracy, providing signal wavelength, λsignal =1053 nm, and idler wavelength, λidler =1075
nm, and used the output of the cw DRO as the input to the ARR. The output from the cw DRO (∼1W) was extracted using an output coupler (OC)
of transmission ∼3% placed between M2 and M4 . We observed the output
from the ARR in time domain using the InGaAs photo-detector (20 GHz, 18.5
ps) and the fast oscilloscope (3.5 GHz, 40 GS/s). The result is shown in Fig.
8.5(a). The moment the EOM is switched ON, a finite electric field at 80
MHz is applied to the electro-optic crystal of the EOM, which in turn slightly
modulates the output of the ARR. However, after a while, as seen, the ARR
output is nearly constant when the modulation depth of the EOM is kept at
µ1 =0 while adjusting the modulation frequency to ν=80 MHz. With the increase in modulation depth from 0 to maximum, the ARR produces distinct
output modulation with constant repetition rate, but increasing amplitude.
As evident from Fig. 8.5(b), at the maximum modulation depth, µ5 =2.4 rads,
the output pulse duration is 3.9 ns at 80 MHz, determined by the resonant
frequency of the EOM.
In a conventional ARR, as described in section 4.1 of chapter 4, the power
transmitted out of the ring (T ARR ) and the power reflected from the ring towards the input beam (RARR ) are constant and depend on the ratio of transmittance (T ) and reflectance (R) of the beam-splitter. However, by modulating the phase of the clockwise and counter-clockwise beams in the ARR, one
can introduce a time delay in the modulated signals. The recombination of
these clockwise and counter-clockwise phase-modulated signals then leads to
the conversion of internal phase modulation into amplitude modulation. This
Chapter 8. Mode-locked, cw OPOs
139
Figure 8.5: (a) Temporal output of the phase-modulated ARR when deployed external to
the DRO. (b) Zoomed temporal output for maximum modulation depth.
140
8.3. Mode-locking of cw DRO using ARR interferometer
concept has been earlier reported in the context of lasers [91].
8.3.3
Mode-locked pulse generation
In order to actively mode-lock the cw DRO, we incorporated the phase-modulated
ARR into the DRO cavity. With the crystal temperature kept at 51.5 o C, the
cw DRO with the ARR and EOM incorporated provides an output power of
262 mW for 9.7 W of pump power and has an oscillation threshold of 3.5 W.
The higher oscillation threshold power as compared to conventional DRO cavity is mainly attributed to the losses introduced by EOM, ARR elements and
longer cavity length.
We then activated the EOM, and systematically changed the modulation
depth of the EOM, while monitoring the modulation frequency simultaneously.
The output of the DRO from ARR is monitored in time domain for different
modulation depths at modulation frequency of ν ± ∆ν. This change in modulation frequency (∆ν) on either side of the EOM resonant frequency is very
small and is of the order of kHz. Figure 8.6(a) shows the temporal output.
At µ1 =0, some perturbation is seen, however with the increase in modulation
depth to µ2 =1.63 rads, pulses of 780 ps duration with 160 MHz repetition rate
are observed. These pulses even shorten down to 730 ps when we increase the
modulation depth to µ3 =1.83 rads. With the increase in modulation depth to
µ4 =1.99 rads, pulses with alternatively equal amplitude are observed with high
intensity pulses at 790 ps and low intensity pulses at 580 ps duration. Further
increase in modulation depth to the maximum value leads to the generation
of pulses with repetition rate of 80 MHz and pulse duration of 450 ps. Figure
8.6(b) and 8.6(c) shows the zoomed version of stable pulses at repetition rate
of 160 MHz and 80 MHz, respectively.
Pulses with 80 MHz repetition rate are also observed when modulation
depth is kept fixed at µ3 =1.83 rads and modulation frequency is changed to
Chapter 8. Mode-locked, cw OPOs
141
Figure 8.6: (a) Pulse train obtained with increase in modulation depth, at modulation
frequency of ν ± ∆ν. (b) Zoomed 730 ps pulses at 160 MHz repetition rate. (c) Zoomed 450
ps pulses at 80 MHz repetition rate.
142
8.3. Mode-locking of cw DRO using ARR interferometer
ν ± ∆ν 0 . The change in modulation frequency, ∆ν 0 , is again of the order of
kHz, where ∆ν 0 > ∆ν. The effect of change in modulation frequency, while
keeping modulation depth fixed at µ3 =1.83 rads, is shown in Fig. 8.7.
As evident, at ν −∆ν 0 , stable pulses of 450 ps duration at 80 MHz repetition
are generated. If the modulation frequency is increased to ν, which is the
resonant frequency of the EOM, a strong perturbation is observed, without
any pulse formation. However, with further increase in modulation frequency
to ν + ∆ν 0 , stable pulses at 80 MHz repetition rate with pulse duration of 550
ps are observed again.
It is thus evident that to obtain stable short pulses at 160 MHz and 80 MHz
repetition rate, a careful adjustment of the modulation frequency or precise
change in cavity length over a narrow zone at higher value of modulation depth
is required.
Figure 8.7: Temporal output at modulation depth of µ3 =1.83 rads and modulation frequencies of (i) ν − ∆ν 0 , (ii) ν, and (iii) ν + ∆ν 0 .
Chapter 8. Mode-locked, cw OPOs
8.3.4
143
Output spectrum
We also measured the DRO output spectrum under three operating conditions,
cw operation (EOM switched OFF), and mode-locked when generating 160
MHz and 80 MHz repetition rate pulses. The results are shown in Fig. 8.8. In
cw operation, we recorded relatively narrow signal and idler spectra centered
at 1053 nm and 1075 nm, respectively. However, for the 160 MHz pulses
spectral broadening over 12 nm is observed about signal (1045-1057 nm) and
idler (1071-1083 nm). On the other hand, for the 80 MHz pulses the signal and
idler branches lock together and form a single broadband spectrum spanning
34 nm over 1047-1081 nm. Similar broadening of the spectra is observed when
the separation between the signal and idler wavelengths is slightly varied by
temperature tuning the cw DRO away from degeneracy. If we tune the cw
DRO to degeneracy by tuning the temperature to 50 o C, further bandwidth
broadening is observed. Figure 8.9 shows the results at degeneracy. As seen,
during cw operation, the signal and idler are centered at 1058 nm and 1070
nm, respectively. However, under mode-locked operation the signal and idler
become locked and broadened over 1045-1083 nm and 1054-1074 nm for 160
MHz and 80 MHz pulses, respectively. The difference in the amplitude of signal
and idler spectrum is attributed to the difference in crystal coating losses and
mirror reflectivities. Assuming Gaussian pulse shape and a time-bandwidth
product of 0.44, the transform limited pulse duration for 34 nm bandwidth
spectrum has been calculated to be ∼48 fs. Clearly, the observed broadband
spectrum is not fully contributing to the generation of the output ps pulses.
Further reduction in pulse width may require higher modulation frequency as
well as dispersion control.
8.3.5
Confirmation of true mode-locked operation
To confirm true mode-locked operation, we performed external single-pass
144
8.3. Mode-locking of cw DRO using ARR interferometer
Figure 8.8: Spectrum of the cw, and mode-locked signal corresponding to 160 MHz (ν ± ∆ν)
and 80 MHz (ν ± ∆ν 0 ) pulses, extracted from the DRO near degeneracy at T =51.5 o C.
Figure 8.9: Spectrum of the cw, and mode-locked signal corresponding to 160 MHz (ν ± ∆ν)
and 80 MHz (ν ± ∆ν 0 ) pulses, extracted from the DRO at T =50 o C.
Chapter 8. Mode-locked, cw OPOs
145
second-harmonic-generation (SHG) of DRO output in a 10-mm-long β-BaB2 O4
(BBO) crystal cut at θ=26o , φ=0o . Using a GaAsP photodetector, we recorded
the SHG output for cw and mode-locked operation corresponding to 160 MHz
and 80 MHz repetition rate pulses. For a fixed average input power to the
BBO crystal, we recorded ∼4 times enhancement in the measured SHG output under mode-locked operation at both 160 MHz and 80 MHz compared to
cw operation, indicating the real achievement of energy concentration resulting from mode-locked operation. The results are shown in Fig. 8.10(a) and
8.10(b). However, the lower than theoretically predicted SHG enhancement
could be attributed to the limited wavelength acceptance bandwidth of the
10-mm-long BBO crystal compared to the spectral width of the OPO output.
Figure 8.10: Enhancement of the SHG output for mode-locked operation with respect to cw
operation, detected using a photodetector for (a) 160 MHz pulses (ν ± ∆ν) and (b) 80 MHz
pulses (ν ± ∆ν 0 ).
8.4
8.4.1
Phase-modulation-mode-locked cw DRO
Experimental setup
The schematic of the experimental setup is shown in Fig. 8.11. The fundamental pump source used is similar to that described in section 8.3.1. To maintain
stable output characteristics of the laser, we operated the pump laser at max-
146
8.4. Phase-modulation-mode-locked cw DRO
imum power and used a combination of a HWP and a PBS cube as power
attenuator. A second HWP is used to adjust the pump polarization for phasematching in the nonlinear crystal. The nonlinear crystal used is identical to
that described in section 8.3.1. The crystal is housed in an oven, with a stability of ±0.1o C, which can be tuned from room temperature to 200 o C. Using
a lens of focal length f =150 mm, the pump beam is focused to waist radius
w p =31 µm corresponding to a confocal focusing parameter of ξ∼1.2, with
signal/idler beam waist radius of w s/i =46 µm at the center of the nonlinear
crystal, resulting into optimum mode matching. The cw DRO is configured in
a standing-wave cavity comprising of two concave mirrors M1 and M2 (r=100
mm), one plane mirror M3 , one concave mirror M4 (r=1000 mm), and one
OC, M5 . Mirrors M1 and M2 are highly reflecting (R>99%) for signal and
idler at 1000-1090 nm and transmitting (T >93%) at 532 nm, while mirrors
M3 and M4 are highly reflecting at 1000-1233 nm (R>99.9%) and 1000-1165
nm (R>99.7%) wavelength range, respectively. The OC has a reflectivity of
R∼96.5% at 1064 nm. Thus, the reflectivity of the mirrors ensures doublyresonant oscillation near degeneracy. The output of the DRO is extracted
through the OC. The EOM, described in section 8.2, is introduced inside the
cavity close to the OC. The distance between the EOM end face and OC is
z 0 =1 cm. The beam diameter through the EOM can be adjusted using mirror
M4 . Mirror, M3 has been mounted over a translation stage, so as to adjust
the cavity length to synchronize with the modulator resonant frequency. The
total optical length of the DRO, when synchronized with resonant frequency
of the phase modulator, is L=2Llinear =3.7 m.
8.4.2
Output power and threshold
With the crystal temperature (T ) kept at 51.5 o C, the DRO without EOM
provides an output power of 526 mW for 9.7 W of pump power and has an
oscillation threshold of 1.1 W. However, with the insertion of the EOM, the
Chapter 8. Mode-locked, cw OPOs
147
Figure 8.11: Schematic of the experimental setup. λ/2: Half-wave plate, PBS: Polarizing
beam-splitter, L: Lens, M: Cavity mirrors, OC: Output coupler; EOM: Electro-optic phase
modulator.
oscillation threshold increases to 1.9 W and the cw DRO provides 484 mW of
output power for a pump power of 9.7 W. The increase in threshold power is
attributed to the EOM insertion loss. It is to be noted that the oscillation
threshold power for DRO in standing-wave configuration having shorter cavity
length, comprising of three high reflecting mirrors and one OC is 700 mW.
The increase in threshold pump power from 700 mW to 1.1 W is attributed
to the additional cavity mirror. At T =51.5 o C the generated signal and idler
wavelengths are λsignal =1049 nm and λidler =1079 nm, respectively. At these
wavelengths, the parametric gain curve of the nonlinear crystal is calculated
to have a FWHM bandwidth of 3 THz.
8.4.3
Mode-locked pulse generation
When the EOM is switched ON, with modulation depth of 1.83 rads and frequency, ν exactly matching with the cavity length, some perturbation is seen in
the output in time domain, but no mode-locked pulses are observed. However,
when the modulation frequency is slightly detuned by ∆ν, on either side of ν,
471 ps pulses at 160 MHz repetition rate are observed. Figure 8.12(a) shows
the temporal output from DRO, at modulation frequency of ν ± ∆ν, depicting
the effect of change in modulation depth. As evident, in (i) at minimum mod-
148
8.4. Phase-modulation-mode-locked cw DRO
ulation, some perturbation is seen, but with increase in modulation depth to
1.63 rads in (ii), 871 ps pulses at 160 MHz are observed, which then shortens
to 471 ps at 1.83 rads of modulation depth in (iii). With further increase in
modulation depth to 1.99 rads in (iv), alternatively equal amplitude pulses at
160 MHz are observed with high intensity pulses at 473 ps duration and low
intensity pulses at 437 ps duration. In (v), with the modulation frequency kept
fixed at ν ± ∆ν, if we further increase the modulation depth to maximum at
2.4 rads, 533 ps pulses at 80 MHz are observed. Pulses at 80 MHz with 533
ps duration are also observed, as shown in Fig. 8.12(b), when the modulation
depth is kept fixed at µ3 =1.83 rads and modulation frequency is detuned by
∆ν 0 , on either side of ν, where ∆ν 0 > ∆ν. The values for ∆ν 0 and ∆ν and
difference between them, are of the order of kHz. Hence, to obtain stable short
pulses at 80 MHz, a careful adjustment of the modulation frequency or precise
change in cavity length over a narrow zone at moderate value of modulation
depth is required. The use of a piezoelectric transducer (PZT)-driven selftuning mirror as one of the cavity mirror could be very helpful, not only to
fine tune the cavity length to achieve the required repetition rate, but also to
actively stabilize the cavity length, thus reducing the possibility of any arbitrary switching of the repetition rate between 80 MHz and 160 MHz, if that
may occur. The inset of Fig. 8.12(b) shows the zoomed version of the stable
pulses with 533 ps duration at 80 MHz repetition rate obtained at modulation
depth of 1.83 rads and modulation frequency of ν ± ∆ν 0 . Unlike the earlier
report with cw pumping [60], we have not observed any cw background in the
output pulse intensity.
Depending upon the temporal characteristics, the region of operation of
the DRO can be divided into two. The two regions can be shown to represent
a series of pulses with one having a repetition rate equal to the modulation
frequency and other at twice that of modulation frequency. As also observed
earlier in the context of lasers [129], here when the train of pulses at 160 MHz
Chapter 8. Mode-locked, cw OPOs
149
Figure 8.12: (a) Pulse train obtained at modulation frequency of ν ±∆ν, and for modulation
depths of (i) µ1 (ii) µ2 (iii) µ3 (iv) µ4 and (v) µ5 . (b) Pulse train obtained at modulation
frequency of ν ± ∆ν 0 and for modulation depth of µ3 . Inset: Zoomed 533 ps pulses at 80
MHz.
150
8.4. Phase-modulation-mode-locked cw DRO
is compared with the sinusoidal modulation signal, the optical phase difference
between the pulses is found to be π. This shows two pulses travelling back and
forth inside the cavity, with one pulse delayed in time by Llinear /c with respect
to the other. Thus, it represents two oscillating states of mode-locked pulses.
For 80 MHz pulses obtained, the pulses pass through the modulator either at
the peak or minima of the modulation signal. The two mode-locked states are
clearly visible at modulation frequency of ν ±∆ν and depth of µ3 =1.99 rads, as
seen in (iv) of Fig. 8.12(a), where alternatively equal pulses are observed with
one state having higher intensity than the other. The two oscillating states
with unequal amplitude are also observed when the modulation depth and
frequency are kept fixed at 1.83 rads and ν ± ∆ν, respectively, while slightly
detuning the cavity length.
8.4.4
Power stability
We recorded the average passive power stability at mode-locked condition for
160 MHz repetition rate pulses at maximum pump power for modulation depth
of 1.83 rads and frequency at ν ± ∆ν. As evident from Fig. 8.13, an average passive power stability better than 3.5% rms over 15 minutes has been
observed. The fluctuation in the average power is attributed to the mechanical vibrations, air currents, and temperature variations, as the measurements
were taken in open laboratory environment and under free running condition
of the DRO. The corresponding pulse train recorded in the microsecond scale,
depicting the intensity noise on the output pulses, is shown in the inset of Fig.
8.13, where a pulse peak-to-peak stability better than 19% is measured over 20
µs. The pulse width measured at end of 20 µs is the same as in the beginning,
showing steady state pulse durations over microsecond time scale.
Chapter 8. Mode-locked, cw OPOs
151
Figure 8.13: Time trace of the mode-locked output at 160 MHz over 15 minutes. Inset:
Mode-locked output pulse train at 160 MHz over 20 µs.
8.4.5
Pulse width dependence on the position of EOM
In order to study the dependence of the pulse width on the position of the EOM
inside the cavity, we increased the distance of the EOM from OC to z 0 =6 cm,
and observed the output from DRO in time domain for different modulation
conditions. The behavior of the output from the DRO is similar as compared
to when EOM is placed very close to OC (z 0 =1 cm), except the difference in
the pulse width. Figure 8.14 shows the pulses obtained at modulation depth
of 1.83 rads and modulation frequency at ν ± ∆ν for z 0 =6 cm, and the inset
of Fig. 8.14 shows the comparison for (i) z 0 =6 cm and (ii) z 0 =1 cm with the
zoomed version of the pulses. As observed, the pulse duration for z 0 =6 cm
is 953 ps, which is larger than the pulse duration obtained for z 0 =1 cm. As
also shown earlier in the context of lasers, the modulation coupling has direct
dependence on the location of the modulation element inside the cavity [129].
When the EOM is very close to the cavity mirror, z 0 ∼0, the coefficient in the
coupled equation [129] is maximized, showing increase in locking of the modes.
152
8.4. Phase-modulation-mode-locked cw DRO
Figure 8.14: Pulse train at 160 MHz for z 0 =6 cm. Inset: Zoomed 953 ps and 471 ps pulses
for (i) z 0 =6 cm and (ii) z 0 =1 cm, respectively.
8.4.6
Pulse width dependence on pumping level
We also looked into the duration of pulses for different input pump power
keeping z 0 =6 cm. We have observed very less significant change in pulse
duration with the change in the pumping level. For example, we measured a
decrease in pulse duration from 953 ps to 848 ps at 160 MHz for a decrease in
pump power from 9.7 W to 6.8 W, accompanied with the decrease in the pulse
amplitude. The OPO stops working with further decrease in pump power to
3.4 W.
8.4.7
Output spectrum
We further looked into the spectral domain under cw and mode-locked condition using spectrometer (HR4000 oceanoptics). Figure 8.15(a) shows the
output spectrum of the DRO under cw operation. Under cw condition the
modes are oscillating independently, with an observed spectral bandwidth of
11 nm and 10 nm for signal and idler, respectively. However, when the modulation depth is increased to 1.83 rads and frequency tuned to ν ±∆ν, a spectrum
Chapter 8. Mode-locked, cw OPOs
153
with almost the same bandwidth as in cw has been observed for signal and
idler, but with an envelope, as seen in Fig. 8.15(b). The lower intensity of
idler is due to the low reflectivity value of cavity concave mirrors for idler
wavelength.
Figure 8.15: Spectrum of the output extracted from the DRO at T =51.5 o C, under (a) cw
operation, and (b) mode-locked operation at modulation frequency of ν ± ∆ν and depth of
µ3 =1.83 rads.
If we decrease the crystal temperature to T =50 o C, keeping modulation
frequency at ν ± ∆ν and depth at µ=1.83 rads, at degeneracy the signal
and idler branches meet together resulting in a spectrum spanning over 31
nm, as seen in Fig 8.16(a). When the modulation frequency is detuned to ν,
the spectrum broadens to its maximum, with an observed increase in average
power. The result is shown in Fig. 8.16(b), where a spectrum spanning over 52
nm is measured at T =50 o C. The corresponding measurement in time domain
showed only some perturbation with no mode-locking, however at modulation
frequency of ν ± ∆ν, pulses are observed with the same duration as at T =51.5
o
C.
Assuming Gaussian pulse shape and a time-bandwidth product of 0.44,
the transform limited pulse duration for 31 nm bandwidth spectrum has been
calculated to be ∼53 fs. Also, considering the internal phase modulation that
result in to a linear frequency shift, as discussed in earlier reports [61], leading
to a time-bandwidth product of 0.626, the pulse duration has been calculated
154
8.4. Phase-modulation-mode-locked cw DRO
Figure 8.16: Spectrum of the output extracted from the DRO at T =50 o C, for modulation
depth of µ3 =1.83 rads, and at modulation frequencies of (a) ν ± ∆ν and (b) ν=80 MHz.
to be ∼75 fs. The discrepancy between the experimental pulse duration and
the transform limited pulse duration could be due to the lower modulation
frequency of the EOM, which results into less efficient mode-locking as all of the
modes in the spectrum does not get locked in phase. The longer pulse duration
obtained could also be due to the intracavity dispersion which comes into
effect because of the longer nonlinear crystal and longer electro-optic crystal
used. Further shorter pulses could be attained using modulator with high
speed modulation and also by using nonlinear crystals with shorter interaction
length, as the DROs are not affected much with lower gain, subject to the low
oscillation threshold power. Use of dispersive or chirp mirrors could also be
useful.
8.4.8
Confirmation of true mode-locked operation
For confirming the mode-locked operation, we performed the external singlepass SHG of the DRO output at different operating conditions. The nonlinear
crystal used is 10-mm-long BBO cut at θ=26o , φ=0o . Using a lens of focal
length, f =75 mm, the output for cw, 160 MHz and 80 MHz pulses was focused
consecutively at the centre of the crystal, and the frequency-doubled power
was measured using the GaAsP photodetector. We have observed ∼4 times
enhancement of the SHG power in mode-locked operation both for 80 and
Chapter 8. Mode-locked, cw OPOs
155
160 MHz pulses, as compared to that in the cw operation, for a fixed average
fundamental power in both conditions. The SHG enhancement factor of ∼4
times is lower than that of the theoretically calculated value of 23 times, for
533 ps pulses at 80 MHz. As we have not observed any cw background with the
mode-locked pulses, we believe that the cw background has negligible effect on
the measured SHG enhancement factor. However, the low SHG enhancement
could be attributed to various factors including narrow acceptance bandwidth
of BBO, as also discussed in section 8.3.5.
8.5
8.5.1
Phase-modulation-mode-locked cw SRO
Experimental setup
The experimental configuration of the mode-locked cw SRO, as shown in Fig.
8.17, is identical to that of the mode-locked cw DRO described in section
8.4.1, except the cavity mirrors used here. Here, mirrors, M1 and M2 , are
highly reflecting for the idler (R>99.9% over 1064–1292 nm) and transmitting
for the signal (T >75%–90% over 800–1000 nm) and pump (T >86% at 532
nm). Mirror, M3 is highly reflecting for the idler (R>99.9% over 1064–1245
nm). Mirror, M4 is reflective for the idler (R>99.7%) only across the 1064–1155
nm wavelength range, while M5 is highly reflecting for the idler (R>99.9%)
over 1064–1245 nm. Thus, the mirrors reflectivity ensures idler-only resonant
configuration. The nonlinear crystal used is identical to that described in
section 8.3.1. The crystal is housed in an oven with a stability of ±0.1 o C,
enabling the temperature to be varied from 25 o C to 200 o C. Using a lens
of focal length, f =150 mm, the pump beam is focused to waist radius of
w p =31 µm, corresponding to a confocal focusing parameter of ξ∼1.2. The
SRO cavity provides an idler beam waist of w i =46 µm, resulting in optimum
mode matching (bp ∼bi ) at the center of the crystal. We use the idler-resonant
design for the SRO to minimize intracavity losses due to the AR-coating range
156
8.5. Phase-modulation-mode-locked cw SRO
(1–1.6 µm) of the EOM deployed for mode-locking. The EOM, described in
section 8.2, is introduced inside the cavity close to the mirror, M5 . The singlepass insertion loss of the EOM is measured to be ∼5% (−0.23 dB) at 1032
nm. The beam diameter through the EOM can be adjusted using mirror M4 .
Mirror, M3 is mounted on a translation stage to enable adjustment of the
cavity length for synchronization with the EOM resonant frequency. The total
SRO cavity length is L=3.7 m, synchronized to the EOM resonant frequency.
A dichroic mirror, M, is used to separate the non-resonant signal from the
transmitted pump.
Figure 8.17: Schematic of the experimental setup. λ/2: Half-wave plate, PBS: Polarizing
beam-splitter, L: Lens, M1−5 : Cavity mirrors, M: Dichroic mirror, EOM: Electro-optic phase
modulator.
8.5.2
Mode-locked pulse generation
We investigated mode-locking of the SRO output by performing systematic
change in the modulation depth of the EOM, while simultaneously studying
the fine adjustment of modulation frequency and accurate change in the cavity
length.
Maintaining the crystal temperature at 70 o C, corresponding to a signal
wavelength of 989 nm (idler of 1151 nm), we monitored the temporal output
of the SRO using the InGaAs photodetector (20 GHz, 18.5 ps) and the fast
oscilloscope (3.5 GHz, 40 GS/s). At these wavelengths, the parametric gain
Chapter 8. Mode-locked, cw OPOs
157
bandwidth for the crystal is 0.6 THz. The SRO oscillation threshold power
was 7.15 W and the data were collected for both the resonant idler (extracted
through mirror M5 ) and the non-resonant signal (extracted through M2 ) at a
pump power of 9.62 W.
When the EOM incorporated inside the SRO cavity is switched on, with
the modulation frequency and depth kept at the minimum value, a slight
sinusoidal modulation is observed in the cw SRO output in time. With the
increase in modulation depth to µ0 =0.18 rads, a modulated output at 80 MHz
repetition frequency is observed. Figure 8.18 shows measurements for the idler
output, depicting the effect of change in modulation frequency and depth,
keeping either of the parameters fixed. In (i), with the modulation depth
fixed at µ0 =0.18 rads, increasing the modulation frequency from minimum to
ν1 results in the generation of 720 ps pulses at 160 MHz. Then, in (ii), by
increasing the modulation frequency to 80 MHz (ν) short pulses of 230 ps
duration at 80 MHz repetition rate are generated. With further increase in
modulation frequency from 80 MHz to ν2 , in (iii), the pulse repetition rate
again changes to 160 MHz. The change in modulation frequency (∆ν = ν − ν1
or ν2 −ν) is very small, of the order of kHz, and corresponds to very narrow zone
for change in the cavity length. The use of a PZT-driven self-tuning mirror
could be helpful for sensitive control of the cavity length. Thus, to obtain
stable short pulses at 80 MHz, perfect synchronization of the cavity length
(free spectral range, FSR=c/L) with the EOM resonant frequency or careful
adjustment of the modulation frequency is required. At marginally lower and
higher modulation frequencies than ν1 and ν2 , respectively, broader pulses
at 160 MHz are generated. On the other hand, by keeping the modulation
frequency fixed at ν (80 MHz) and reducing modulation depth from µ0 =0.18
rads to a lower value (µ00 ), we observe 620 ps pulses at 160 MHz, as seen in
(iv). Further decrease in modulation depth to µ000 results in broadening of the
pulses to 1.4 ns, as seen in (v).
158
8.5. Phase-modulation-mode-locked cw SRO
Figure 8.18: Idler output pulse train obtained at modulation frequency (ν1 <ν<ν2 ) and
modulation depth (µ0 >µ00 >µ000 ) of (i) ν1 , µ0 ; (ii) ν, µ0 ; (iii) ν2 , µ0 ; (iv) ν, µ00 ; (v) ν, µ000 .
Figure 8.19 shows the applied sinusoidal modulation (at µ0 =0.18 rads) together with resonant idler pulses obtained at the exact modulation frequency
of 80 MHz (ν), and at slight detuning (ν1 , ν2 ). As evident, for 80 MHz pulses
(obtained at ν), the pulses appears at alternating values of 0 and 2π. Thus,
the optical phase difference between the pulses is 2π. However, for 160 MHz
pulses (obtained at ν1 , ν2 ), the phase difference is observed to be π. This indicates that a slight detuning of modulation frequency from synchronization can
lead to pulses with twice the repetition rate. At the modulation frequency of
80 MHz (ν), a single phase-locked state oscillates inside the cavity, but as the
modulation frequency is increased or decreased by ∆ν, double pulsing occurs
with two mode-locked states oscillating together. Similar behavior was also
observed for the non-resonant signal wave.
Figures 8.20(a) and 8.20(b) show the output signal pulses at modulation
depth of µ0 =0.18 rads with repetition frequency of 160 and 80 MHz obtained
at modulation frequency of ν1 and ν, respectively. As seen, pulses as short as
737 ps at 160 MHz and 288 ps at 80 MHz were recorded, exhibiting a similar
Chapter 8. Mode-locked, cw OPOs
159
Figure 8.19: (a) Applied modulation, (b) 80 MHz, and (c) 160 MHz repetition rate idler
pulses at µ0 =0.18 rads.
behavior to the idler pulses. Also, as evident, there is no cw background
present in the idler or signal pulse intensity.
Figure 8.20: Signal pulses at (a) 160 MHz and (b) 80 MHz.
As compared to the pulse width obtained, in section 8.4.3 from mode-locked
cw DRO, we observed shorter pulses in SRO configuration. We believe that the
difference in the pulse duration could be due to the phase modulator used in the
experiment, which are specified for narrowband or single-frequency operation.
160
8.5. Phase-modulation-mode-locked cw SRO
As we have seen in section 8.4.6, and also there are earlier reports [47] showing
effect of pump power on pulse duration, the difference in the pulse duration
could also be due to the higher pumping level (5 times above threshold) in the
DRO as compared to that in the SRO.
8.5.3
Output spectrum
Using a FPI (FSR=1 GHz, finesse=400), we measured the spectrum of the
mode-locked signal output. As shown in Fig. 8.21, under mode-locked condition (µ0 =0.18 rads; ν1 ) we found the spectrum to extend across ∆f ∼0.619
GHz. The corresponding transform-limited pulse duration is calculated to be
∆τ ∼710 ps, assuming Gaussian pulse shape and a time-bandwidth product of
∆τ · ∆f =0.44. However, it has been shown that internal phase modulation
results in a linear frequency shift, which leads to a timebandwidth product
of 0.626 [61]. Considering the frequency chirp and low FSR of our FPI, we
believe the spectrum to be broader than what we observe. In mode-locked
operation at 80 MHz repetition rate, the signal spectral bandwidth could not
be determined, as the measurement was limited by the diagnostics.
Figure 8.21: Spectrum of the mode-locked signal at 160 MHz.
Chapter 8. Mode-locked, cw OPOs
8.5.4
161
Pulse stability, and confirmation of true mode-locked
operation
We also determined the stability of the mode-locked output pulse train by
recording the intensity noise on the signal pulses at 80 MHz. The result is
shown in Fig. 8.22, where a pulse peak-to-peak stability better than 15% is
measured over 500 µs.
Figure 8.22: Signal pulse train at 80 MHz over 500 µs.
Further, in order to confirm true mode-locked operation of the SRO, we
performed external single-pass SHG in 10-mm-long BBO crystal cut at θ=26o ,
φ=0o and AR-coated for 425–500 nm and 850–1000 nm. The output signal
was focused at the center of the crystal in both mode-locked and cw operation
using same lens of focal length, f =75 mm, and the frequency-doubled output
in the blue was recorded using the GaAsP photodetector. Using this setup,
we observed a ∼4 times enhancement of SHG power in mode-locked operation
compared to that in cw operation, for the same average fundamental power in
both conditions.
162
8.6
8.6. Conclusions
Conclusions
In conclusion, we have demonstrated, what we believe for the first time, the
generation of picosecond pulses from cw OPOs using novel techniques based
on phase modulation assisted amplitude modulation, and also by pure phase
modulation.
By deploying an electro-optic phase modulator and an ARR interferometer
internal to a near-degenerate cw DRO based on MgO:sPPLT, we generated
730 ps pulses at 160 MHz and 450 ps pulses at 80 MHz. Spectral broadening
spanning ∼34 nm has also been observed. We have also demonstrated the
generation of picosecond pulses from a cw DRO based on MgO:sPPLT by
active mode-locking of the DRO using an electro-optic phase modulator as the
single mode-locking element. Mode-locked pulses at 80 MHz and 160 MHz
with 533 ps and 471 ps pulse duration at modulation depth of 1.83 rads and
modulation frequency at ν ±∆ν 0 and ν ±∆ν, respectively, have been generated.
Mode-locked pulses for different operating regions of the DRO, obtained with
the change in modulation depth and frequency detuning have been explored.
It has also been observed that like in lasers, in OPO cavity the position of the
modulator is an important factor for obtaining shorter pulses. The average
passive power stability of the DRO output for 160 MHz has been measured
to be better than 3.5% rms over 15 minutes. Under moderate modulation
depth and at exact resonant frequency modulation, spectrum spanning over
52 nm has been observed at degeneracy. The mode-locked operation has been
further confirmed by observing ∼4 times enhancement in SHG power under
mode-locked condition, as compared to cw operation.
Further, we have demonstrated successful mode-locking of a cw SRO using direct electro-optic phase modulation, providing output pulses as short as
230 ps at 80 MHz repetition rate. Mode-locked pulses obtained for different
operating regions of the SRO have been explored.
Chapter 8. Mode-locked, cw OPOs
163
By using an EOM with increased modulation frequency and by deploying intracavity dispersion compensation, further reductions in pulse duration
could be attainable. The extension of the approach to passive mode-locking
techniques, including Kerr-lens mode-locking, will pave the way for the realization of a new generation of ultrafast sources with broad and arbitrary tuning
in different spectral regions based on OPOs pumped by widely available cw
lasers.
Chapter 9
Summary and outlook
In this thesis, we have demonstrated the development of optical parametric oscillators (OPOs), and nonlinear frequency conversion sources, under continuouswave (cw) pumping, spanning the ultraviolet (UV) to mid-infrared (IR) spectral regions. Different architectures, designs, experimental configurations and
nonlinear crystals have been deployed and investigated, for the first time.
The main outcomes of the work include:
• Demonstration of an efficient fiber-laser-based source of high-power, cw,
linearly-polarized radiation at 970 nm in a simple, compact, and practical
design. Using direct single-pass second-harmonic-generation (SP-SHG),
13.1 W of output power at 970 nm has been generated for a fundamental
power of 40 W at a conversion efficiency as high as 32.7%. The generated
second-harmonic output exhibits a passive power stability better than
1.4% (1σ value) over 1 hour, has a linewidth better than 0.3 nm, and
a TEM00 spatial beam profile with M 2 <1.6. Relevant theoretical calculations for the characterization of SP-SHG in the crystal have also been
performed.
• Successful deployment of an antiresonant ring (ARR) interferometer for
166
the attainment of optimum output coupling in a Yb-fiber-laser-pumped
cw OPO. The cw OPO, configured as a singly-resonant oscillator (SRO),
was based on MgO:PPLN. By fine adjustment of the ARR transmission, a
continuously variable signal output coupling from 0.8% to 7.3% has been
achieved, providing optimum output coupling for signal and optimum
power extraction for the idler, at different input pumping levels. The
experimental results were further compared with theoretical calculations
for conventional output-coupled cw SRO.
• Demonstration of a high-power, single-frequency, cw source tunable across
775-807 nm in the near-infrared, based on internal second-harmonic-generation
(SHG) of a cw SRO pumped by a Yb-fiber laser. The compact, allperiodically-poled source provides as much as 3.7 W of near-infrared
power at 793 nm, together with 4 W of idler power at 3232 nm, at an overall extraction efficiency of 28%. Further, the cw OPO is tunable across
3125-3396 nm in the idler, providing as much as 4.3 W at 3133 nm with
>3.8 W over 77% of the tuning range together with >3 W of near-infrared
power across 56% of SHG tuning range, in high spatial beam quality with
M 2 <1.4. The SHG output has an instantaneous linewidth of 8.5 MHz
and exhibits a passive power stability better than 3.5% rms over more
than one minute.
• Generation of stable, cw UV radiation in single-pass configuration based
on sum-frequency-mixing of 1064 nm and 532 nm radiation, in BiB3 O6 .
The 532 nm radiation was generated by single-pass SHG of Yb-fiber laser
in MgO:sPPLT. The single-pass cw UV source provides as much as 68
mW of single-frequency UV power with a passive power stability better
than 3.2% rms over 2 hours and frequency stability better than 437 MHz
over >2.5 hours, in elliptic beam profile with M x 2 <1.6 and M y 2 <1.8,
indicating a TEM00 spatial mode.
• A novel architecture comprising two cw OPOs coupled together with an
Chapter 9. Summary and outlook
167
ARR interferometer, generating two pairs of signal and idler wavelengths.
The OPOs, based on identical MgO:sPPLT crystals, were pumped by a
single cw laser at 532 nm. The two pairs of signal and idler wavelengths
can be independently and arbitrarily tuned to indefinitely close spacing,
through degeneracy, and beyond, across the wavelength range of 8701370 nm. Frequency separation from 7 THz down to 0.8 THz has been
demonstrated, and their overlap at 951 nm shown, providing a frequency
difference of ∼220 MHz. The OPOs simultaneously generated idler powers
of >1 W.
• Generation of record shortest picosecond pulses by active mode-locking of
cw OPOs in doubly- and singly-resonant configuration using direct lowfrequency electro-optic phase-modulation (EOM). Also, a technique based
on the deployment of the EOM in combination with an ARR interferometer internal to the cw OPO has been investigated. The mode-locking of
cw SRO has resulted in a stable train of 230 ps pulses at 80 MHz.
As a direction for the future work, the performance of the OPOs in terms of
power stability can further be improved by better temperature control, isolation from mechanical vibrations, and active stabilization of cavity length. The
theoretical study of the output-coupled SRO shows that by reducing the insertion loss of the ARR elements, the performance of the ARR output-coupled
cw SRO can be further enhanced. The demonstrated SHG tuning in the nearinfrared can be further extended to cover almost the entire Ti:sapphire wavelength range using different grating periods of the employed MgO:PPLN crystal and simultaneously varying the grating of the MgO:sPPLT crystal. In the
ARR-coupled OPO, the high intracavity power of the two closely spaced, unidirectional signal waves can be used for efficient generation of widely tunable
terahertz radiation. New nonlinear materials for cw terahertz generation can
be explored.
168
Future possible developments of this work include:
• Development of Tm-fiber-laser-pumped cw OPOs tunable in the spectral
region beyond 4 µm, based on MgO:PPLN and OP-GaAs
• The deployment of intracavity sum-frequency-mixing scheme in green-
laser-pumped cw OPO, resulting in the generation of tunable UV radiation.
• Active mode-locking of cw OPO using an EOM with increased modulation
frequency, and various crystal lengths.
Investigations in these directions are already ongoing.
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